[{"data":1,"prerenderedAt":5264},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-heron":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-heron":5251},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":247,"checks":5141,"conditions":5164,"conditionsHtml":5165,"deprecated":5166,"description":5134,"extension":5167,"figure":5168,"figureCaption":5169,"figureHtml":5218,"formulaId":5219,"latex":5220,"latexHtml":5221,"level":5222,"meta":5223,"navigation":5187,"path":5224,"redirectFrom":5225,"related":5226,"seo":5231,"stem":5232,"subject":595,"summary":5233,"tags":5234,"variables":5239,"__hash__":5250},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-heron.md","Satz des Heron",[550,551,552,553,554],"Heronsche Formel","Heron Formel","Dreiecksfläche aus drei Seiten","Flächeninhalt Dreieck ohne Höhe","halber Umfang",{"type":556,"value":557,"toc":5133},"minimark",[558,563,571,574,977,1135,1139,1729,2099,2801,2805,3008,3398,3565,3819,4063,4257,4758,4762],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,570],"p",{},"Mit dem ",[568,569,548],"strong",{}," berechnet man den Flächeninhalt eines Dreiecks, wenn nur die drei Seitenlängen bekannt sind. Man braucht weder eine Höhe noch einen Winkel.",[564,572,573],{},"Vorgehen:",[575,576,577,782,945],"ol",{},[578,579,580,581,584,585,781],"li",{},"Den ",[568,582,583],{},"halben Umfang"," ",[586,587,590,640],"span",{"className":588},[589],"katex",[586,591,594],{"className":592},[593],"katex-mathml",[595,596,598],"math",{"xmlns":597},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[599,600,601,635],"semantics",{},[602,603,604,608,612],"mrow",{},[605,606,607],"mi",{},"s",[609,610,611],"mo",{},"=",[613,614,615,631],"mfrac",{},[602,616,617,620,623,626,628],{},[605,618,619],{},"a",[609,621,622],{},"+",[605,624,625],{},"b",[609,627,622],{},[605,629,630],{},"c",[632,633,634],"mn",{},"2",[636,637,639],"annotation",{"encoding":638},"application\u002Fx-tex","s = \\frac{a + b + c}{2}",[586,641,645,671],{"className":642,"ariaHidden":644},[643],"katex-html","true",[586,646,649,654,659,664,668],{"className":647},[648],"base",[586,650],{"className":651,"style":653},[652],"strut","height:0.4306em;",[586,655,607],{"className":656},[657,658],"mord","mathnormal",[586,660],{"className":661,"style":663},[662],"mspace","margin-right:0.2778em;",[586,665,611],{"className":666},[667],"mrel",[586,669],{"className":670,"style":663},[662],[586,672,674,678],{"className":673},[648],[586,675],{"className":676,"style":677},[652],"height:1.2251em;vertical-align:-0.345em;",[586,679,681,686,777],{"className":680},[657],[586,682],{"className":683},[684,685],"mopen","nulldelimiter",[586,687,689],{"className":688},[613],[586,690,694,768],{"className":691},[692,693],"vlist-t","vlist-t2",[586,695,698,763],{"className":696},[697],"vlist-r",[586,699,703,724,735],{"className":700,"style":702},[701],"vlist","height:0.8801em;",[586,704,706,711],{"style":705},"top:-2.655em;",[586,707],{"className":708,"style":710},[709],"pstrut","height:3em;",[586,712,718],{"className":713},[714,715,716,717],"sizing","reset-size6","size3","mtight",[586,719,721],{"className":720},[657,717],[586,722,634],{"className":723},[657,717],[586,725,727,730],{"style":726},"top:-3.23em;",[586,728],{"className":729,"style":710},[709],[586,731],{"className":732,"style":734},[733],"frac-line","border-bottom-width:0.04em;",[586,736,738,741],{"style":737},"top:-3.394em;",[586,739],{"className":740,"style":710},[709],[586,742,744],{"className":743},[714,715,716,717],[586,745,747,750,754,757,760],{"className":746},[657,717],[586,748,619],{"className":749},[657,658,717],[586,751,622],{"className":752},[753,717],"mbin",[586,755,625],{"className":756},[657,658,717],[586,758,622],{"className":759},[753,717],[586,761,630],{"className":762},[657,658,717],[586,764,767],{"className":765},[766],"vlist-s","​",[586,769,771],{"className":770},[697],[586,772,775],{"className":773,"style":774},[701],"height:0.345em;",[586,776],{},[586,778],{"className":779},[780,685],"mclose"," berechnen.",[578,783,784,785,839,840,892,893,944],{},"Die drei Differenzen ",[586,786,788,807],{"className":787},[589],[586,789,791],{"className":790},[593],[595,792,793],{"xmlns":597},[599,794,795,804],{},[602,796,797,799,802],{},[605,798,607],{},[609,800,801],{},"−",[605,803,619],{},[636,805,806],{"encoding":638},"s - a",[586,808,810,830],{"className":809,"ariaHidden":644},[643],[586,811,813,817,820,824,827],{"className":812},[648],[586,814],{"className":815,"style":816},[652],"height:0.6667em;vertical-align:-0.0833em;",[586,818,607],{"className":819},[657,658],[586,821],{"className":822,"style":823},[662],"margin-right:0.2222em;",[586,825,801],{"className":826},[753],[586,828],{"className":829,"style":823},[662],[586,831,833,836],{"className":832},[648],[586,834],{"className":835,"style":653},[652],[586,837,619],{"className":838},[657,658],", ",[586,841,843,861],{"className":842},[589],[586,844,846],{"className":845},[593],[595,847,848],{"xmlns":597},[599,849,850,858],{},[602,851,852,854,856],{},[605,853,607],{},[609,855,801],{},[605,857,625],{},[636,859,860],{"encoding":638},"s - b",[586,862,864,882],{"className":863,"ariaHidden":644},[643],[586,865,867,870,873,876,879],{"className":866},[648],[586,868],{"className":869,"style":816},[652],[586,871,607],{"className":872},[657,658],[586,874],{"className":875,"style":823},[662],[586,877,801],{"className":878},[753],[586,880],{"className":881,"style":823},[662],[586,883,885,889],{"className":884},[648],[586,886],{"className":887,"style":888},[652],"height:0.6944em;",[586,890,625],{"className":891},[657,658]," und ",[586,894,896,914],{"className":895},[589],[586,897,899],{"className":898},[593],[595,900,901],{"xmlns":597},[599,902,903,911],{},[602,904,905,907,909],{},[605,906,607],{},[609,908,801],{},[605,910,630],{},[636,912,913],{"encoding":638},"s - c",[586,915,917,935],{"className":916,"ariaHidden":644},[643],[586,918,920,923,926,929,932],{"className":919},[648],[586,921],{"className":922,"style":816},[652],[586,924,607],{"className":925},[657,658],[586,927],{"className":928,"style":823},[662],[586,930,801],{"className":931},[753],[586,933],{"className":934,"style":823},[662],[586,936,938,941],{"className":937},[648],[586,939],{"className":940,"style":653},[652],[586,942,630],{"className":943},[657,658]," bilden.",[578,946,947,948,976],{},"Alles mit ",[586,949,951,964],{"className":950},[589],[586,952,954],{"className":953},[593],[595,955,956],{"xmlns":597},[599,957,958,962],{},[602,959,960],{},[605,961,607],{},[636,963,607],{"encoding":638},[586,965,967],{"className":966,"ariaHidden":644},[643],[586,968,970,973],{"className":969},[648],[586,971],{"className":972,"style":653},[652],[586,974,607],{"className":975},[657,658]," multiplizieren und die Wurzel ziehen.",[564,978,979,980,983,984,839,1034,839,1084,1134],{},"Die Formel gilt nur, wenn die drei Längen wirklich ein Dreieck bilden: Jede Seite muss kürzer sein als die beiden anderen zusammen (",[568,981,982],{},"Dreiecksungleichung","). Dann sind alle Differenzen ",[586,985,987,1004],{"className":986},[589],[586,988,990],{"className":989},[593],[595,991,992],{"xmlns":597},[599,993,994,1002],{},[602,995,996,998,1000],{},[605,997,607],{},[609,999,801],{},[605,1001,619],{},[636,1003,806],{"encoding":638},[586,1005,1007,1025],{"className":1006,"ariaHidden":644},[643],[586,1008,1010,1013,1016,1019,1022],{"className":1009},[648],[586,1011],{"className":1012,"style":816},[652],[586,1014,607],{"className":1015},[657,658],[586,1017],{"className":1018,"style":823},[662],[586,1020,801],{"className":1021},[753],[586,1023],{"className":1024,"style":823},[662],[586,1026,1028,1031],{"className":1027},[648],[586,1029],{"className":1030,"style":653},[652],[586,1032,619],{"className":1033},[657,658],[586,1035,1037,1054],{"className":1036},[589],[586,1038,1040],{"className":1039},[593],[595,1041,1042],{"xmlns":597},[599,1043,1044,1052],{},[602,1045,1046,1048,1050],{},[605,1047,607],{},[609,1049,801],{},[605,1051,625],{},[636,1053,860],{"encoding":638},[586,1055,1057,1075],{"className":1056,"ariaHidden":644},[643],[586,1058,1060,1063,1066,1069,1072],{"className":1059},[648],[586,1061],{"className":1062,"style":816},[652],[586,1064,607],{"className":1065},[657,658],[586,1067],{"className":1068,"style":823},[662],[586,1070,801],{"className":1071},[753],[586,1073],{"className":1074,"style":823},[662],[586,1076,1078,1081],{"className":1077},[648],[586,1079],{"className":1080,"style":888},[652],[586,1082,625],{"className":1083},[657,658],[586,1085,1087,1104],{"className":1086},[589],[586,1088,1090],{"className":1089},[593],[595,1091,1092],{"xmlns":597},[599,1093,1094,1102],{},[602,1095,1096,1098,1100],{},[605,1097,607],{},[609,1099,801],{},[605,1101,630],{},[636,1103,913],{"encoding":638},[586,1105,1107,1125],{"className":1106,"ariaHidden":644},[643],[586,1108,1110,1113,1116,1119,1122],{"className":1109},[648],[586,1111],{"className":1112,"style":816},[652],[586,1114,607],{"className":1115},[657,658],[586,1117],{"className":1118,"style":823},[662],[586,1120,801],{"className":1121},[753],[586,1123],{"className":1124,"style":823},[662],[586,1126,1128,1131],{"className":1127},[648],[586,1129],{"className":1130,"style":653},[652],[586,1132,630],{"className":1133},[657,658]," positiv.",[559,1136,1138],{"id":1137},"herleitung","Herleitung",[564,1140,1141,1142,1299,1300,1562,1563,1728],{},"Aus ",[586,1143,1145,1182],{"className":1144},[589],[586,1146,1148],{"className":1147},[593],[595,1149,1150],{"xmlns":597},[599,1151,1152,1179],{},[602,1153,1154,1157,1159,1166,1168,1170,1173,1176],{},[605,1155,1156],{},"A",[609,1158,611],{},[613,1160,1161,1164],{},[632,1162,1163],{},"1",[632,1165,634],{},[605,1167,619],{},[605,1169,625],{},[605,1171,1172],{},"sin",[609,1174,1175],{},"⁡",[605,1177,1178],{},"γ",[636,1180,1181],{"encoding":638},"A = \\frac{1}{2} a b \\sin \\gamma",[586,1183,1185,1204],{"className":1184,"ariaHidden":644},[643],[586,1186,1188,1192,1195,1198,1201],{"className":1187},[648],[586,1189],{"className":1190,"style":1191},[652],"height:0.6833em;",[586,1193,1156],{"className":1194},[657,658],[586,1196],{"className":1197,"style":663},[662],[586,1199,611],{"className":1200},[667],[586,1202],{"className":1203,"style":663},[662],[586,1205,1207,1211,1280,1284,1288,1292,1295],{"className":1206},[648],[586,1208],{"className":1209,"style":1210},[652],"height:1.1901em;vertical-align:-0.345em;",[586,1212,1214,1217,1277],{"className":1213},[657],[586,1215],{"className":1216},[684,685],[586,1218,1220],{"className":1219},[613],[586,1221,1223,1269],{"className":1222},[692,693],[586,1224,1226,1266],{"className":1225},[697],[586,1227,1230,1244,1252],{"className":1228,"style":1229},[701],"height:0.8451em;",[586,1231,1232,1235],{"style":705},[586,1233],{"className":1234,"style":710},[709],[586,1236,1238],{"className":1237},[714,715,716,717],[586,1239,1241],{"className":1240},[657,717],[586,1242,634],{"className":1243},[657,717],[586,1245,1246,1249],{"style":726},[586,1247],{"className":1248,"style":710},[709],[586,1250],{"className":1251,"style":734},[733],[586,1253,1254,1257],{"style":737},[586,1255],{"className":1256,"style":710},[709],[586,1258,1260],{"className":1259},[714,715,716,717],[586,1261,1263],{"className":1262},[657,717],[586,1264,1163],{"className":1265},[657,717],[586,1267,767],{"className":1268},[766],[586,1270,1272],{"className":1271},[697],[586,1273,1275],{"className":1274,"style":774},[701],[586,1276],{},[586,1278],{"className":1279},[780,685],[586,1281,1283],{"className":1282},[657,658],"ab",[586,1285],{"className":1286,"style":1287},[662],"margin-right:0.1667em;",[586,1289,1172],{"className":1290},[1291],"mop",[586,1293],{"className":1294,"style":1287},[662],[586,1296,1178],{"className":1297,"style":1298},[657,658],"margin-right:0.0556em;"," und dem Kosinussatz ",[586,1301,1303,1359],{"className":1302},[589],[586,1304,1306],{"className":1305},[593],[595,1307,1308],{"xmlns":597},[599,1309,1310,1356],{},[602,1311,1312,1315,1317,1319,1321],{},[605,1313,1314],{},"cos",[609,1316,1175],{},[605,1318,1178],{},[609,1320,611],{},[613,1322,1323,1348],{},[602,1324,1325,1332,1334,1340,1342],{},[1326,1327,1328,1330],"msup",{},[605,1329,619],{},[632,1331,634],{},[609,1333,622],{},[1326,1335,1336,1338],{},[605,1337,625],{},[632,1339,634],{},[609,1341,801],{},[1326,1343,1344,1346],{},[605,1345,630],{},[632,1347,634],{},[602,1349,1350,1352,1354],{},[632,1351,634],{},[605,1353,619],{},[605,1355,625],{},[636,1357,1358],{"encoding":638},"\\cos \\gamma = \\frac{a^2 + b^2 - c^2}{2ab}",[586,1360,1362,1387],{"className":1361,"ariaHidden":644},[643],[586,1363,1365,1369,1372,1375,1378,1381,1384],{"className":1364},[648],[586,1366],{"className":1367,"style":1368},[652],"height:0.625em;vertical-align:-0.1944em;",[586,1370,1314],{"className":1371},[1291],[586,1373],{"className":1374,"style":1287},[662],[586,1376,1178],{"className":1377,"style":1298},[657,658],[586,1379],{"className":1380,"style":663},[662],[586,1382,611],{"className":1383},[667],[586,1385],{"className":1386,"style":663},[662],[586,1388,1390,1394],{"className":1389},[648],[586,1391],{"className":1392,"style":1393},[652],"height:1.3629em;vertical-align:-0.345em;",[586,1395,1397,1400,1559],{"className":1396},[657],[586,1398],{"className":1399},[684,685],[586,1401,1403],{"className":1402},[613],[586,1404,1406,1551],{"className":1405},[692,693],[586,1407,1409,1548],{"className":1408},[697],[586,1410,1413,1430,1438],{"className":1411,"style":1412},[701],"height:1.0179em;",[586,1414,1415,1418],{"style":705},[586,1416],{"className":1417,"style":710},[709],[586,1419,1421],{"className":1420},[714,715,716,717],[586,1422,1424,1427],{"className":1423},[657,717],[586,1425,634],{"className":1426},[657,717],[586,1428,1283],{"className":1429},[657,658,717],[586,1431,1432,1435],{"style":726},[586,1433],{"className":1434,"style":710},[709],[586,1436],{"className":1437,"style":734},[733],[586,1439,1440,1443],{"style":737},[586,1441],{"className":1442,"style":710},[709],[586,1444,1446],{"className":1445},[714,715,716,717],[586,1447,1449,1484,1487,1516,1519],{"className":1448},[657,717],[586,1450,1452,1455],{"className":1451},[657,717],[586,1453,619],{"className":1454},[657,658,717],[586,1456,1459],{"className":1457},[1458],"msupsub",[586,1460,1462],{"className":1461},[692],[586,1463,1465],{"className":1464},[697],[586,1466,1469],{"className":1467,"style":1468},[701],"height:0.8913em;",[586,1470,1472,1476],{"style":1471},"top:-2.931em;margin-right:0.0714em;",[586,1473],{"className":1474,"style":1475},[709],"height:2.5em;",[586,1477,1481],{"className":1478},[714,1479,1480,717],"reset-size3","size1",[586,1482,634],{"className":1483},[657,717],[586,1485,622],{"className":1486},[753,717],[586,1488,1490,1493],{"className":1489},[657,717],[586,1491,625],{"className":1492},[657,658,717],[586,1494,1496],{"className":1495},[1458],[586,1497,1499],{"className":1498},[692],[586,1500,1502],{"className":1501},[697],[586,1503,1505],{"className":1504,"style":1468},[701],[586,1506,1507,1510],{"style":1471},[586,1508],{"className":1509,"style":1475},[709],[586,1511,1513],{"className":1512},[714,1479,1480,717],[586,1514,634],{"className":1515},[657,717],[586,1517,801],{"className":1518},[753,717],[586,1520,1522,1525],{"className":1521},[657,717],[586,1523,630],{"className":1524},[657,658,717],[586,1526,1528],{"className":1527},[1458],[586,1529,1531],{"className":1530},[692],[586,1532,1534],{"className":1533},[697],[586,1535,1537],{"className":1536,"style":1468},[701],[586,1538,1539,1542],{"style":1471},[586,1540],{"className":1541,"style":1475},[709],[586,1543,1545],{"className":1544},[714,1479,1480,717],[586,1546,634],{"className":1547},[657,717],[586,1549,767],{"className":1550},[766],[586,1552,1554],{"className":1553},[697],[586,1555,1557],{"className":1556,"style":774},[701],[586,1558],{},[586,1560],{"className":1561},[780,685]," folgt mit ",[586,1564,1566,1608],{"className":1565},[589],[586,1567,1569],{"className":1568},[593],[595,1570,1571],{"xmlns":597},[599,1572,1573,1605],{},[602,1574,1575,1585,1587,1589,1591,1593,1603],{},[1326,1576,1577,1583],{},[602,1578,1579,1581],{},[605,1580,1172],{},[609,1582,1175],{},[632,1584,634],{},[605,1586,1178],{},[609,1588,611],{},[632,1590,1163],{},[609,1592,801],{},[1326,1594,1595,1601],{},[602,1596,1597,1599],{},[605,1598,1314],{},[609,1600,1175],{},[632,1602,634],{},[605,1604,1178],{},[636,1606,1607],{"encoding":638},"\\sin^2 \\gamma = 1 - \\cos^2 \\gamma",[586,1609,1611,1665,1684],{"className":1610,"ariaHidden":644},[643],[586,1612,1614,1618,1650,1653,1656,1659,1662],{"className":1613},[648],[586,1615],{"className":1616,"style":1617},[652],"height:1.0663em;vertical-align:-0.1944em;",[586,1619,1621,1624],{"className":1620},[1291],[586,1622,1172],{"className":1623},[1291],[586,1625,1627],{"className":1626},[1458],[586,1628,1630],{"className":1629},[692],[586,1631,1633],{"className":1632},[697],[586,1634,1637],{"className":1635,"style":1636},[701],"height:0.8719em;",[586,1638,1640,1644],{"style":1639},"top:-3.1208em;margin-right:0.05em;",[586,1641],{"className":1642,"style":1643},[709],"height:2.7em;",[586,1645,1647],{"className":1646},[714,715,716,717],[586,1648,634],{"className":1649},[657,717],[586,1651],{"className":1652,"style":1287},[662],[586,1654,1178],{"className":1655,"style":1298},[657,658],[586,1657],{"className":1658,"style":663},[662],[586,1660,611],{"className":1661},[667],[586,1663],{"className":1664,"style":663},[662],[586,1666,1668,1672,1675,1678,1681],{"className":1667},[648],[586,1669],{"className":1670,"style":1671},[652],"height:0.7278em;vertical-align:-0.0833em;",[586,1673,1163],{"className":1674},[657],[586,1676],{"className":1677,"style":823},[662],[586,1679,801],{"className":1680},[753],[586,1682],{"className":1683,"style":823},[662],[586,1685,1687,1691,1722,1725],{"className":1686},[648],[586,1688],{"className":1689,"style":1690},[652],"height:1.0085em;vertical-align:-0.1944em;",[586,1692,1694,1697],{"className":1693},[1291],[586,1695,1314],{"className":1696},[1291],[586,1698,1700],{"className":1699},[1458],[586,1701,1703],{"className":1702},[692],[586,1704,1706],{"className":1705},[697],[586,1707,1710],{"className":1708,"style":1709},[701],"height:0.8141em;",[586,1711,1713,1716],{"style":1712},"top:-3.063em;margin-right:0.05em;",[586,1714],{"className":1715,"style":1643},[709],[586,1717,1719],{"className":1718},[714,715,716,717],[586,1720,634],{"className":1721},[657,717],[586,1723],{"className":1724,"style":1287},[662],[586,1726,1178],{"className":1727,"style":1298},[657,658],":",[586,1730,1733],{"className":1731},[1732],"katex-display",[586,1734,1736,1811],{"className":1735},[589],[586,1737,1739],{"className":1738},[593],[595,1740,1742],{"xmlns":597,"display":1741},"block",[599,1743,1744,1808],{},[602,1745,1746,1749,1755,1757,1760,1766,1772,1774],{},[632,1747,1748],{},"16",[1326,1750,1751,1753],{},[605,1752,1156],{},[632,1754,634],{},[609,1756,611],{},[632,1758,1759],{},"4",[1326,1761,1762,1764],{},[605,1763,619],{},[632,1765,634],{},[1326,1767,1768,1770],{},[605,1769,625],{},[632,1771,634],{},[609,1773,801],{},[1326,1775,1776,1806],{},[602,1777,1778,1781,1787,1789,1795,1797,1803],{},[609,1779,1780],{"fence":644},"(",[1326,1782,1783,1785],{},[605,1784,619],{},[632,1786,634],{},[609,1788,622],{},[1326,1790,1791,1793],{},[605,1792,625],{},[632,1794,634],{},[609,1796,801],{},[1326,1798,1799,1801],{},[605,1800,630],{},[632,1802,634],{},[609,1804,1805],{"fence":644},")",[632,1807,634],{},[636,1809,1810],{"encoding":638},"16 A^2 = 4a^2b^2 - \\left(a^2 + b^2 - c^2\\right)^2",[586,1812,1814,1863,1940],{"className":1813,"ariaHidden":644},[643],[586,1815,1817,1821,1824,1854,1857,1860],{"className":1816},[648],[586,1818],{"className":1819,"style":1820},[652],"height:0.8641em;",[586,1822,1748],{"className":1823},[657],[586,1825,1827,1830],{"className":1826},[657],[586,1828,1156],{"className":1829},[657,658],[586,1831,1833],{"className":1832},[1458],[586,1834,1836],{"className":1835},[692],[586,1837,1839],{"className":1838},[697],[586,1840,1842],{"className":1841,"style":1820},[701],[586,1843,1845,1848],{"style":1844},"top:-3.113em;margin-right:0.05em;",[586,1846],{"className":1847,"style":1643},[709],[586,1849,1851],{"className":1850},[714,715,716,717],[586,1852,634],{"className":1853},[657,717],[586,1855],{"className":1856,"style":663},[662],[586,1858,611],{"className":1859},[667],[586,1861],{"className":1862,"style":663},[662],[586,1864,1866,1870,1873,1902,1931,1934,1937],{"className":1865},[648],[586,1867],{"className":1868,"style":1869},[652],"height:0.9474em;vertical-align:-0.0833em;",[586,1871,1759],{"className":1872},[657],[586,1874,1876,1879],{"className":1875},[657],[586,1877,619],{"className":1878},[657,658],[586,1880,1882],{"className":1881},[1458],[586,1883,1885],{"className":1884},[692],[586,1886,1888],{"className":1887},[697],[586,1889,1891],{"className":1890,"style":1820},[701],[586,1892,1893,1896],{"style":1844},[586,1894],{"className":1895,"style":1643},[709],[586,1897,1899],{"className":1898},[714,715,716,717],[586,1900,634],{"className":1901},[657,717],[586,1903,1905,1908],{"className":1904},[657],[586,1906,625],{"className":1907},[657,658],[586,1909,1911],{"className":1910},[1458],[586,1912,1914],{"className":1913},[692],[586,1915,1917],{"className":1916},[697],[586,1918,1920],{"className":1919,"style":1820},[701],[586,1921,1922,1925],{"style":1844},[586,1923],{"className":1924,"style":1643},[709],[586,1926,1928],{"className":1927},[714,715,716,717],[586,1929,634],{"className":1930},[657,717],[586,1932],{"className":1933,"style":823},[662],[586,1935,801],{"className":1936},[753],[586,1938],{"className":1939,"style":823},[662],[586,1941,1943,1947],{"className":1942},[648],[586,1944],{"className":1945,"style":1946},[652],"height:1.4181em;vertical-align:-0.35em;",[586,1948,1951,2074],{"className":1949},[1950],"minner",[586,1952,1954,1963,1992,1995,1998,2001,2030,2033,2036,2039,2068],{"className":1953},[1950],[586,1955,1959],{"className":1956,"style":1958},[684,1957],"delimcenter","top:0em;",[586,1960,1780],{"className":1961},[1962,1480],"delimsizing",[586,1964,1966,1969],{"className":1965},[657],[586,1967,619],{"className":1968},[657,658],[586,1970,1972],{"className":1971},[1458],[586,1973,1975],{"className":1974},[692],[586,1976,1978],{"className":1977},[697],[586,1979,1981],{"className":1980,"style":1820},[701],[586,1982,1983,1986],{"style":1844},[586,1984],{"className":1985,"style":1643},[709],[586,1987,1989],{"className":1988},[714,715,716,717],[586,1990,634],{"className":1991},[657,717],[586,1993],{"className":1994,"style":823},[662],[586,1996,622],{"className":1997},[753],[586,1999],{"className":2000,"style":823},[662],[586,2002,2004,2007],{"className":2003},[657],[586,2005,625],{"className":2006},[657,658],[586,2008,2010],{"className":2009},[1458],[586,2011,2013],{"className":2012},[692],[586,2014,2016],{"className":2015},[697],[586,2017,2019],{"className":2018,"style":1820},[701],[586,2020,2021,2024],{"style":1844},[586,2022],{"className":2023,"style":1643},[709],[586,2025,2027],{"className":2026},[714,715,716,717],[586,2028,634],{"className":2029},[657,717],[586,2031],{"className":2032,"style":823},[662],[586,2034,801],{"className":2035},[753],[586,2037],{"className":2038,"style":823},[662],[586,2040,2042,2045],{"className":2041},[657],[586,2043,630],{"className":2044},[657,658],[586,2046,2048],{"className":2047},[1458],[586,2049,2051],{"className":2050},[692],[586,2052,2054],{"className":2053},[697],[586,2055,2057],{"className":2056,"style":1820},[701],[586,2058,2059,2062],{"style":1844},[586,2060],{"className":2061,"style":1643},[709],[586,2063,2065],{"className":2064},[714,715,716,717],[586,2066,634],{"className":2067},[657,717],[586,2069,2071],{"className":2070,"style":1958},[780,1957],[586,2072,1805],{"className":2073},[1962,1480],[586,2075,2077],{"className":2076},[1458],[586,2078,2080],{"className":2079},[692],[586,2081,2083],{"className":2082},[697],[586,2084,2087],{"className":2085,"style":2086},[701],"height:1.0681em;",[586,2088,2090,2093],{"style":2089},"top:-3.317em;margin-right:0.05em;",[586,2091],{"className":2092,"style":1643},[709],[586,2094,2096],{"className":2095},[714,715,716,717],[586,2097,634],{"className":2098},[657,717],[564,2100,2101,2102,2427,2428,839,2456,839,2506,2556,2557,2607,2608,2800],{},"Zweimal die dritte binomische Formel angewendet ergibt ",[586,2103,2105,2186],{"className":2104},[589],[586,2106,2108],{"className":2107},[593],[595,2109,2110],{"xmlns":597},[599,2111,2112,2183],{},[602,2113,2114,2116,2122,2124,2127,2129,2131,2133,2135,2137,2139,2141,2143,2145,2147,2149,2151,2153,2155,2157,2159,2161,2163,2165,2167,2169,2171,2173,2175,2177,2179,2181],{},[632,2115,1748],{},[1326,2117,2118,2120],{},[605,2119,1156],{},[632,2121,634],{},[609,2123,611],{},[609,2125,1780],{"stretchy":2126},"false",[605,2128,619],{},[609,2130,622],{},[605,2132,625],{},[609,2134,622],{},[605,2136,630],{},[609,2138,1805],{"stretchy":2126},[609,2140,1780],{"stretchy":2126},[609,2142,801],{},[605,2144,619],{},[609,2146,622],{},[605,2148,625],{},[609,2150,622],{},[605,2152,630],{},[609,2154,1805],{"stretchy":2126},[609,2156,1780],{"stretchy":2126},[605,2158,619],{},[609,2160,801],{},[605,2162,625],{},[609,2164,622],{},[605,2166,630],{},[609,2168,1805],{"stretchy":2126},[609,2170,1780],{"stretchy":2126},[605,2172,619],{},[609,2174,622],{},[605,2176,625],{},[609,2178,801],{},[605,2180,630],{},[609,2182,1805],{"stretchy":2126},[636,2184,2185],{"encoding":638},"16 A^2 = (a + b + c)(-a + b + c)(a - b + c)(a + b - c)",[586,2187,2189,2236,2258,2277,2307,2325,2352,2370,2397,2415],{"className":2188,"ariaHidden":644},[643],[586,2190,2192,2195,2198,2227,2230,2233],{"className":2191},[648],[586,2193],{"className":2194,"style":1709},[652],[586,2196,1748],{"className":2197},[657],[586,2199,2201,2204],{"className":2200},[657],[586,2202,1156],{"className":2203},[657,658],[586,2205,2207],{"className":2206},[1458],[586,2208,2210],{"className":2209},[692],[586,2211,2213],{"className":2212},[697],[586,2214,2216],{"className":2215,"style":1709},[701],[586,2217,2218,2221],{"style":1712},[586,2219],{"className":2220,"style":1643},[709],[586,2222,2224],{"className":2223},[714,715,716,717],[586,2225,634],{"className":2226},[657,717],[586,2228],{"className":2229,"style":663},[662],[586,2231,611],{"className":2232},[667],[586,2234],{"className":2235,"style":663},[662],[586,2237,2239,2243,2246,2249,2252,2255],{"className":2238},[648],[586,2240],{"className":2241,"style":2242},[652],"height:1em;vertical-align:-0.25em;",[586,2244,1780],{"className":2245},[684],[586,2247,619],{"className":2248},[657,658],[586,2250],{"className":2251,"style":823},[662],[586,2253,622],{"className":2254},[753],[586,2256],{"className":2257,"style":823},[662],[586,2259,2261,2265,2268,2271,2274],{"className":2260},[648],[586,2262],{"className":2263,"style":2264},[652],"height:0.7778em;vertical-align:-0.0833em;",[586,2266,625],{"className":2267},[657,658],[586,2269],{"className":2270,"style":823},[662],[586,2272,622],{"className":2273},[753],[586,2275],{"className":2276,"style":823},[662],[586,2278,2280,2283,2286,2289,2292,2295,2298,2301,2304],{"className":2279},[648],[586,2281],{"className":2282,"style":2242},[652],[586,2284,630],{"className":2285},[657,658],[586,2287,1805],{"className":2288},[780],[586,2290,1780],{"className":2291},[684],[586,2293,801],{"className":2294},[657],[586,2296,619],{"className":2297},[657,658],[586,2299],{"className":2300,"style":823},[662],[586,2302,622],{"className":2303},[753],[586,2305],{"className":2306,"style":823},[662],[586,2308,2310,2313,2316,2319,2322],{"className":2309},[648],[586,2311],{"className":2312,"style":2264},[652],[586,2314,625],{"className":2315},[657,658],[586,2317],{"className":2318,"style":823},[662],[586,2320,622],{"className":2321},[753],[586,2323],{"className":2324,"style":823},[662],[586,2326,2328,2331,2334,2337,2340,2343,2346,2349],{"className":2327},[648],[586,2329],{"className":2330,"style":2242},[652],[586,2332,630],{"className":2333},[657,658],[586,2335,1805],{"className":2336},[780],[586,2338,1780],{"className":2339},[684],[586,2341,619],{"className":2342},[657,658],[586,2344],{"className":2345,"style":823},[662],[586,2347,801],{"className":2348},[753],[586,2350],{"className":2351,"style":823},[662],[586,2353,2355,2358,2361,2364,2367],{"className":2354},[648],[586,2356],{"className":2357,"style":2264},[652],[586,2359,625],{"className":2360},[657,658],[586,2362],{"className":2363,"style":823},[662],[586,2365,622],{"className":2366},[753],[586,2368],{"className":2369,"style":823},[662],[586,2371,2373,2376,2379,2382,2385,2388,2391,2394],{"className":2372},[648],[586,2374],{"className":2375,"style":2242},[652],[586,2377,630],{"className":2378},[657,658],[586,2380,1805],{"className":2381},[780],[586,2383,1780],{"className":2384},[684],[586,2386,619],{"className":2387},[657,658],[586,2389],{"className":2390,"style":823},[662],[586,2392,622],{"className":2393},[753],[586,2395],{"className":2396,"style":823},[662],[586,2398,2400,2403,2406,2409,2412],{"className":2399},[648],[586,2401],{"className":2402,"style":2264},[652],[586,2404,625],{"className":2405},[657,658],[586,2407],{"className":2408,"style":823},[662],[586,2410,801],{"className":2411},[753],[586,2413],{"className":2414,"style":823},[662],[586,2416,2418,2421,2424],{"className":2417},[648],[586,2419],{"className":2420,"style":2242},[652],[586,2422,630],{"className":2423},[657,658],[586,2425,1805],{"className":2426},[780],". Jeder Faktor ist das Doppelte von ",[586,2429,2431,2444],{"className":2430},[589],[586,2432,2434],{"className":2433},[593],[595,2435,2436],{"xmlns":597},[599,2437,2438,2442],{},[602,2439,2440],{},[605,2441,607],{},[636,2443,607],{"encoding":638},[586,2445,2447],{"className":2446,"ariaHidden":644},[643],[586,2448,2450,2453],{"className":2449},[648],[586,2451],{"className":2452,"style":653},[652],[586,2454,607],{"className":2455},[657,658],[586,2457,2459,2476],{"className":2458},[589],[586,2460,2462],{"className":2461},[593],[595,2463,2464],{"xmlns":597},[599,2465,2466,2474],{},[602,2467,2468,2470,2472],{},[605,2469,607],{},[609,2471,801],{},[605,2473,619],{},[636,2475,806],{"encoding":638},[586,2477,2479,2497],{"className":2478,"ariaHidden":644},[643],[586,2480,2482,2485,2488,2491,2494],{"className":2481},[648],[586,2483],{"className":2484,"style":816},[652],[586,2486,607],{"className":2487},[657,658],[586,2489],{"className":2490,"style":823},[662],[586,2492,801],{"className":2493},[753],[586,2495],{"className":2496,"style":823},[662],[586,2498,2500,2503],{"className":2499},[648],[586,2501],{"className":2502,"style":653},[652],[586,2504,619],{"className":2505},[657,658],[586,2507,2509,2526],{"className":2508},[589],[586,2510,2512],{"className":2511},[593],[595,2513,2514],{"xmlns":597},[599,2515,2516,2524],{},[602,2517,2518,2520,2522],{},[605,2519,607],{},[609,2521,801],{},[605,2523,625],{},[636,2525,860],{"encoding":638},[586,2527,2529,2547],{"className":2528,"ariaHidden":644},[643],[586,2530,2532,2535,2538,2541,2544],{"className":2531},[648],[586,2533],{"className":2534,"style":816},[652],[586,2536,607],{"className":2537},[657,658],[586,2539],{"className":2540,"style":823},[662],[586,2542,801],{"className":2543},[753],[586,2545],{"className":2546,"style":823},[662],[586,2548,2550,2553],{"className":2549},[648],[586,2551],{"className":2552,"style":888},[652],[586,2554,625],{"className":2555},[657,658]," bzw. ",[586,2558,2560,2577],{"className":2559},[589],[586,2561,2563],{"className":2562},[593],[595,2564,2565],{"xmlns":597},[599,2566,2567,2575],{},[602,2568,2569,2571,2573],{},[605,2570,607],{},[609,2572,801],{},[605,2574,630],{},[636,2576,913],{"encoding":638},[586,2578,2580,2598],{"className":2579,"ariaHidden":644},[643],[586,2581,2583,2586,2589,2592,2595],{"className":2582},[648],[586,2584],{"className":2585,"style":816},[652],[586,2587,607],{"className":2588},[657,658],[586,2590],{"className":2591,"style":823},[662],[586,2593,801],{"className":2594},[753],[586,2596],{"className":2597,"style":823},[662],[586,2599,2601,2604],{"className":2600},[648],[586,2602],{"className":2603,"style":653},[652],[586,2605,630],{"className":2606},[657,658],", also ",[586,2609,2611,2663],{"className":2610},[589],[586,2612,2614],{"className":2613},[593],[595,2615,2616],{"xmlns":597},[599,2617,2618,2660],{},[602,2619,2620,2626,2628,2630,2632,2634,2636,2638,2640,2642,2644,2646,2648,2650,2652,2654,2656,2658],{},[1326,2621,2622,2624],{},[605,2623,1156],{},[632,2625,634],{},[609,2627,611],{},[605,2629,607],{},[609,2631,1780],{"stretchy":2126},[605,2633,607],{},[609,2635,801],{},[605,2637,619],{},[609,2639,1805],{"stretchy":2126},[609,2641,1780],{"stretchy":2126},[605,2643,607],{},[609,2645,801],{},[605,2647,625],{},[609,2649,1805],{"stretchy":2126},[609,2651,1780],{"stretchy":2126},[605,2653,607],{},[609,2655,801],{},[605,2657,630],{},[609,2659,1805],{"stretchy":2126},[636,2661,2662],{"encoding":638},"A^2 = s(s - a)(s - b)(s - c)",[586,2664,2666,2710,2734,2761,2788],{"className":2665,"ariaHidden":644},[643],[586,2667,2669,2672,2701,2704,2707],{"className":2668},[648],[586,2670],{"className":2671,"style":1709},[652],[586,2673,2675,2678],{"className":2674},[657],[586,2676,1156],{"className":2677},[657,658],[586,2679,2681],{"className":2680},[1458],[586,2682,2684],{"className":2683},[692],[586,2685,2687],{"className":2686},[697],[586,2688,2690],{"className":2689,"style":1709},[701],[586,2691,2692,2695],{"style":1712},[586,2693],{"className":2694,"style":1643},[709],[586,2696,2698],{"className":2697},[714,715,716,717],[586,2699,634],{"className":2700},[657,717],[586,2702],{"className":2703,"style":663},[662],[586,2705,611],{"className":2706},[667],[586,2708],{"className":2709,"style":663},[662],[586,2711,2713,2716,2719,2722,2725,2728,2731],{"className":2712},[648],[586,2714],{"className":2715,"style":2242},[652],[586,2717,607],{"className":2718},[657,658],[586,2720,1780],{"className":2721},[684],[586,2723,607],{"className":2724},[657,658],[586,2726],{"className":2727,"style":823},[662],[586,2729,801],{"className":2730},[753],[586,2732],{"className":2733,"style":823},[662],[586,2735,2737,2740,2743,2746,2749,2752,2755,2758],{"className":2736},[648],[586,2738],{"className":2739,"style":2242},[652],[586,2741,619],{"className":2742},[657,658],[586,2744,1805],{"className":2745},[780],[586,2747,1780],{"className":2748},[684],[586,2750,607],{"className":2751},[657,658],[586,2753],{"className":2754,"style":823},[662],[586,2756,801],{"className":2757},[753],[586,2759],{"className":2760,"style":823},[662],[586,2762,2764,2767,2770,2773,2776,2779,2782,2785],{"className":2763},[648],[586,2765],{"className":2766,"style":2242},[652],[586,2768,625],{"className":2769},[657,658],[586,2771,1805],{"className":2772},[780],[586,2774,1780],{"className":2775},[684],[586,2777,607],{"className":2778},[657,658],[586,2780],{"className":2781,"style":823},[662],[586,2783,801],{"className":2784},[753],[586,2786],{"className":2787,"style":823},[662],[586,2789,2791,2794,2797],{"className":2790},[648],[586,2792],{"className":2793,"style":2242},[652],[586,2795,630],{"className":2796},[657,658],[586,2798,1805],{"className":2799},[780],".",[559,2802,2804],{"id":2803},"beispiele","Beispiele",[564,2806,2807,2808,839,2856,892,2898,2941,2942,3007],{},"Dreieck mit den Seiten ",[586,2809,2811,2833],{"className":2810},[589],[586,2812,2814],{"className":2813},[593],[595,2815,2816],{"xmlns":597},[599,2817,2818,2830],{},[602,2819,2820,2823,2827],{},[632,2821,2822],{},"3",[2824,2825,2826],"mtext",{}," ",[2824,2828,2829],{},"cm",[636,2831,2832],{"encoding":638},"3\\,\\text{cm}",[586,2834,2836],{"className":2835,"ariaHidden":644},[643],[586,2837,2839,2843,2846,2849],{"className":2838},[648],[586,2840],{"className":2841,"style":2842},[652],"height:0.6444em;",[586,2844,2822],{"className":2845},[657],[586,2847],{"className":2848,"style":1287},[662],[586,2850,2853],{"className":2851},[657,2852],"text",[586,2854,2829],{"className":2855},[657],[586,2857,2859,2877],{"className":2858},[589],[586,2860,2862],{"className":2861},[593],[595,2863,2864],{"xmlns":597},[599,2865,2866,2874],{},[602,2867,2868,2870,2872],{},[632,2869,1759],{},[2824,2871,2826],{},[2824,2873,2829],{},[636,2875,2876],{"encoding":638},"4\\,\\text{cm}",[586,2878,2880],{"className":2879,"ariaHidden":644},[643],[586,2881,2883,2886,2889,2892],{"className":2882},[648],[586,2884],{"className":2885,"style":2842},[652],[586,2887,1759],{"className":2888},[657],[586,2890],{"className":2891,"style":1287},[662],[586,2893,2895],{"className":2894},[657,2852],[586,2896,2829],{"className":2897},[657],[586,2899,2901,2920],{"className":2900},[589],[586,2902,2904],{"className":2903},[593],[595,2905,2906],{"xmlns":597},[599,2907,2908,2917],{},[602,2909,2910,2913,2915],{},[632,2911,2912],{},"5",[2824,2914,2826],{},[2824,2916,2829],{},[636,2918,2919],{"encoding":638},"5\\,\\text{cm}",[586,2921,2923],{"className":2922,"ariaHidden":644},[643],[586,2924,2926,2929,2932,2935],{"className":2925},[648],[586,2927],{"className":2928,"style":2842},[652],[586,2930,2912],{"className":2931},[657],[586,2933],{"className":2934,"style":1287},[662],[586,2936,2938],{"className":2937},[657,2852],[586,2939,2829],{"className":2940},[657],": ",[586,2943,2945,2968],{"className":2944},[589],[586,2946,2948],{"className":2947},[593],[595,2949,2950],{"xmlns":597},[599,2951,2952,2965],{},[602,2953,2954,2956,2958,2961,2963],{},[605,2955,607],{},[609,2957,611],{},[632,2959,2960],{},"6",[2824,2962,2826],{},[2824,2964,2829],{},[636,2966,2967],{"encoding":638},"s = 6\\,\\text{cm}",[586,2969,2971,2989],{"className":2970,"ariaHidden":644},[643],[586,2972,2974,2977,2980,2983,2986],{"className":2973},[648],[586,2975],{"className":2976,"style":653},[652],[586,2978,607],{"className":2979},[657,658],[586,2981],{"className":2982,"style":663},[662],[586,2984,611],{"className":2985},[667],[586,2987],{"className":2988,"style":663},[662],[586,2990,2992,2995,2998,3001],{"className":2991},[648],[586,2993],{"className":2994,"style":2842},[652],[586,2996,2960],{"className":2997},[657],[586,2999],{"className":3000,"style":1287},[662],[586,3002,3004],{"className":3003},[657,2852],[586,3005,2829],{"className":3006},[657]," und",[586,3009,3011],{"className":3010},[1732],[586,3012,3014,3085],{"className":3013},[589],[586,3015,3017],{"className":3016},[593],[595,3018,3019],{"xmlns":597,"display":1741},[599,3020,3021,3082],{},[602,3022,3023,3025,3027,3047,3049,3055,3057,3062,3064,3070,3072,3074,3076],{},[605,3024,1156],{},[609,3026,611],{},[3028,3029,3030],"msqrt",{},[602,3031,3032,3034,3037,3039,3041,3043,3045],{},[632,3033,2960],{},[609,3035,3036],{},"⋅",[632,3038,2822],{},[609,3040,3036],{},[632,3042,634],{},[609,3044,3036],{},[632,3046,1163],{},[2824,3048,2826],{},[1326,3050,3051,3053],{},[2824,3052,2829],{},[632,3054,634],{},[609,3056,611],{},[3028,3058,3059],{},[632,3060,3061],{},"36",[2824,3063,2826],{},[1326,3065,3066,3068],{},[2824,3067,2829],{},[632,3069,634],{},[609,3071,611],{},[632,3073,2960],{},[2824,3075,2826],{},[1326,3077,3078,3080],{},[2824,3079,2829],{},[632,3081,634],{},[636,3083,3084],{"encoding":638},"A = \\sqrt{6 \\cdot 3 \\cdot 2 \\cdot 1}\\,\\text{cm}^2 = \\sqrt{36}\\,\\text{cm}^2 = 6\\,\\text{cm}^2",[586,3086,3088,3106,3257,3354],{"className":3087,"ariaHidden":644},[643],[586,3089,3091,3094,3097,3100,3103],{"className":3090},[648],[586,3092],{"className":3093,"style":1191},[652],[586,3095,1156],{"className":3096},[657,658],[586,3098],{"className":3099,"style":663},[662],[586,3101,611],{"className":3102},[667],[586,3104],{"className":3105,"style":663},[662],[586,3107,3109,3113,3213,3216,3248,3251,3254],{"className":3108},[648],[586,3110],{"className":3111,"style":3112},[652],"height:1.04em;vertical-align:-0.0839em;",[586,3114,3117],{"className":3115},[657,3116],"sqrt",[586,3118,3120,3204],{"className":3119},[692,693],[586,3121,3123,3201],{"className":3122},[697],[586,3124,3127,3178],{"className":3125,"style":3126},[701],"height:0.9561em;",[586,3128,3132,3135],{"className":3129,"style":3131},[3130],"svg-align","top:-3em;",[586,3133],{"className":3134,"style":710},[709],[586,3136,3139,3142,3145,3148,3151,3154,3157,3160,3163,3166,3169,3172,3175],{"className":3137,"style":3138},[657],"padding-left:0.833em;",[586,3140,2960],{"className":3141},[657],[586,3143],{"className":3144,"style":823},[662],[586,3146,3036],{"className":3147},[753],[586,3149],{"className":3150,"style":823},[662],[586,3152,2822],{"className":3153},[657],[586,3155],{"className":3156,"style":823},[662],[586,3158,3036],{"className":3159},[753],[586,3161],{"className":3162,"style":823},[662],[586,3164,634],{"className":3165},[657],[586,3167],{"className":3168,"style":823},[662],[586,3170,3036],{"className":3171},[753],[586,3173],{"className":3174,"style":823},[662],[586,3176,1163],{"className":3177},[657],[586,3179,3181,3184],{"style":3180},"top:-2.9161em;",[586,3182],{"className":3183,"style":710},[709],[586,3185,3189],{"className":3186,"style":3188},[3187],"hide-tail","min-width:0.853em;height:1.08em;",[3190,3191,3197],"svg",{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[3198,3199],"path",{"d":3200},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[586,3202,767],{"className":3203},[766],[586,3205,3207],{"className":3206},[697],[586,3208,3211],{"className":3209,"style":3210},[701],"height:0.0839em;",[586,3212],{},[586,3214],{"className":3215,"style":1287},[662],[586,3217,3219,3225],{"className":3218},[657],[586,3220,3222],{"className":3221},[657,2852],[586,3223,2829],{"className":3224},[657],[586,3226,3228],{"className":3227},[1458],[586,3229,3231],{"className":3230},[692],[586,3232,3234],{"className":3233},[697],[586,3235,3237],{"className":3236,"style":1820},[701],[586,3238,3239,3242],{"style":1844},[586,3240],{"className":3241,"style":1643},[709],[586,3243,3245],{"className":3244},[714,715,716,717],[586,3246,634],{"className":3247},[657,717],[586,3249],{"className":3250,"style":663},[662],[586,3252,611],{"className":3253},[667],[586,3255],{"className":3256,"style":663},[662],[586,3258,3260,3263,3310,3313,3345,3348,3351],{"className":3259},[648],[586,3261],{"className":3262,"style":3112},[652],[586,3264,3266],{"className":3265},[657,3116],[586,3267,3269,3302],{"className":3268},[692,693],[586,3270,3272,3299],{"className":3271},[697],[586,3273,3275,3287],{"className":3274,"style":3126},[701],[586,3276,3278,3281],{"className":3277,"style":3131},[3130],[586,3279],{"className":3280,"style":710},[709],[586,3282,3284],{"className":3283,"style":3138},[657],[586,3285,3061],{"className":3286},[657],[586,3288,3289,3292],{"style":3180},[586,3290],{"className":3291,"style":710},[709],[586,3293,3295],{"className":3294,"style":3188},[3187],[3190,3296,3297],{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},[3198,3298],{"d":3200},[586,3300,767],{"className":3301},[766],[586,3303,3305],{"className":3304},[697],[586,3306,3308],{"className":3307,"style":3210},[701],[586,3309],{},[586,3311],{"className":3312,"style":1287},[662],[586,3314,3316,3322],{"className":3315},[657],[586,3317,3319],{"className":3318},[657,2852],[586,3320,2829],{"className":3321},[657],[586,3323,3325],{"className":3324},[1458],[586,3326,3328],{"className":3327},[692],[586,3329,3331],{"className":3330},[697],[586,3332,3334],{"className":3333,"style":1820},[701],[586,3335,3336,3339],{"style":1844},[586,3337],{"className":3338,"style":1643},[709],[586,3340,3342],{"className":3341},[714,715,716,717],[586,3343,634],{"className":3344},[657,717],[586,3346],{"className":3347,"style":663},[662],[586,3349,611],{"className":3350},[667],[586,3352],{"className":3353,"style":663},[662],[586,3355,3357,3360,3363,3366],{"className":3356},[648],[586,3358],{"className":3359,"style":1820},[652],[586,3361,2960],{"className":3362},[657],[586,3364],{"className":3365,"style":1287},[662],[586,3367,3369,3375],{"className":3368},[657],[586,3370,3372],{"className":3371},[657,2852],[586,3373,2829],{"className":3374},[657],[586,3376,3378],{"className":3377},[1458],[586,3379,3381],{"className":3380},[692],[586,3382,3384],{"className":3383},[697],[586,3385,3387],{"className":3386,"style":1820},[701],[586,3388,3389,3392],{"style":1844},[586,3390],{"className":3391,"style":1643},[709],[586,3393,3395],{"className":3394},[714,715,716,717],[586,3396,634],{"className":3397},[657,717],[564,3399,3400,3401,2800],{},"Das passt zur Rechnung über die Katheten: ",[586,3402,3404,3434],{"className":3403},[589],[586,3405,3407],{"className":3406},[593],[595,3408,3409],{"xmlns":597},[599,3410,3411,3431],{},[602,3412,3413,3419,3421,3423,3425,3427,3429],{},[613,3414,3415,3417],{},[632,3416,1163],{},[632,3418,634],{},[609,3420,3036],{},[632,3422,2822],{},[609,3424,3036],{},[632,3426,1759],{},[609,3428,611],{},[632,3430,2960],{},[636,3432,3433],{"encoding":638},"\\frac{1}{2} \\cdot 3 \\cdot 4 = 6",[586,3435,3437,3520,3538,3556],{"className":3436,"ariaHidden":644},[643],[586,3438,3440,3443,3511,3514,3517],{"className":3439},[648],[586,3441],{"className":3442,"style":1210},[652],[586,3444,3446,3449,3508],{"className":3445},[657],[586,3447],{"className":3448},[684,685],[586,3450,3452],{"className":3451},[613],[586,3453,3455,3500],{"className":3454},[692,693],[586,3456,3458,3497],{"className":3457},[697],[586,3459,3461,3475,3483],{"className":3460,"style":1229},[701],[586,3462,3463,3466],{"style":705},[586,3464],{"className":3465,"style":710},[709],[586,3467,3469],{"className":3468},[714,715,716,717],[586,3470,3472],{"className":3471},[657,717],[586,3473,634],{"className":3474},[657,717],[586,3476,3477,3480],{"style":726},[586,3478],{"className":3479,"style":710},[709],[586,3481],{"className":3482,"style":734},[733],[586,3484,3485,3488],{"style":737},[586,3486],{"className":3487,"style":710},[709],[586,3489,3491],{"className":3490},[714,715,716,717],[586,3492,3494],{"className":3493},[657,717],[586,3495,1163],{"className":3496},[657,717],[586,3498,767],{"className":3499},[766],[586,3501,3503],{"className":3502},[697],[586,3504,3506],{"className":3505,"style":774},[701],[586,3507],{},[586,3509],{"className":3510},[780,685],[586,3512],{"className":3513,"style":823},[662],[586,3515,3036],{"className":3516},[753],[586,3518],{"className":3519,"style":823},[662],[586,3521,3523,3526,3529,3532,3535],{"className":3522},[648],[586,3524],{"className":3525,"style":2842},[652],[586,3527,2822],{"className":3528},[657],[586,3530],{"className":3531,"style":823},[662],[586,3533,3036],{"className":3534},[753],[586,3536],{"className":3537,"style":823},[662],[586,3539,3541,3544,3547,3550,3553],{"className":3540},[648],[586,3542],{"className":3543,"style":2842},[652],[586,3545,1759],{"className":3546},[657],[586,3548],{"className":3549,"style":663},[662],[586,3551,611],{"className":3552},[667],[586,3554],{"className":3555,"style":663},[662],[586,3557,3559,3562],{"className":3558},[648],[586,3560],{"className":3561,"style":2842},[652],[586,3563,2960],{"className":3564},[657],[564,3566,2807,3567,839,3596,892,3625,2941,3654,3007],{},[586,3568,3570,3584],{"className":3569},[589],[586,3571,3573],{"className":3572},[593],[595,3574,3575],{"xmlns":597},[599,3576,3577,3582],{},[602,3578,3579],{},[632,3580,3581],{},"13",[636,3583,3581],{"encoding":638},[586,3585,3587],{"className":3586,"ariaHidden":644},[643],[586,3588,3590,3593],{"className":3589},[648],[586,3591],{"className":3592,"style":2842},[652],[586,3594,3581],{"className":3595},[657],[586,3597,3599,3613],{"className":3598},[589],[586,3600,3602],{"className":3601},[593],[595,3603,3604],{"xmlns":597},[599,3605,3606,3611],{},[602,3607,3608],{},[632,3609,3610],{},"14",[636,3612,3610],{"encoding":638},[586,3614,3616],{"className":3615,"ariaHidden":644},[643],[586,3617,3619,3622],{"className":3618},[648],[586,3620],{"className":3621,"style":2842},[652],[586,3623,3610],{"className":3624},[657],[586,3626,3628,3642],{"className":3627},[589],[586,3629,3631],{"className":3630},[593],[595,3632,3633],{"xmlns":597},[599,3634,3635,3640],{},[602,3636,3637],{},[632,3638,3639],{},"15",[636,3641,3639],{"encoding":638},[586,3643,3645],{"className":3644,"ariaHidden":644},[643],[586,3646,3648,3651],{"className":3647},[648],[586,3649],{"className":3650,"style":2842},[652],[586,3652,3639],{"className":3653},[657],[586,3655,3657,3694],{"className":3656},[589],[586,3658,3660],{"className":3659},[593],[595,3661,3662],{"xmlns":597},[599,3663,3664,3691],{},[602,3665,3666,3668,3670,3686,3688],{},[605,3667,607],{},[609,3669,611],{},[613,3671,3672,3684],{},[602,3673,3674,3676,3678,3680,3682],{},[632,3675,3581],{},[609,3677,622],{},[632,3679,3610],{},[609,3681,622],{},[632,3683,3639],{},[632,3685,634],{},[609,3687,611],{},[632,3689,3690],{},"21",[636,3692,3693],{"encoding":638},"s = \\frac{13 + 14 + 15}{2} = 21",[586,3695,3697,3715,3810],{"className":3696,"ariaHidden":644},[643],[586,3698,3700,3703,3706,3709,3712],{"className":3699},[648],[586,3701],{"className":3702,"style":653},[652],[586,3704,607],{"className":3705},[657,658],[586,3707],{"className":3708,"style":663},[662],[586,3710,611],{"className":3711},[667],[586,3713],{"className":3714,"style":663},[662],[586,3716,3718,3721,3801,3804,3807],{"className":3717},[648],[586,3719],{"className":3720,"style":1210},[652],[586,3722,3724,3727,3798],{"className":3723},[657],[586,3725],{"className":3726},[684,685],[586,3728,3730],{"className":3729},[613],[586,3731,3733,3790],{"className":3732},[692,693],[586,3734,3736,3787],{"className":3735},[697],[586,3737,3739,3753,3761],{"className":3738,"style":1229},[701],[586,3740,3741,3744],{"style":705},[586,3742],{"className":3743,"style":710},[709],[586,3745,3747],{"className":3746},[714,715,716,717],[586,3748,3750],{"className":3749},[657,717],[586,3751,634],{"className":3752},[657,717],[586,3754,3755,3758],{"style":726},[586,3756],{"className":3757,"style":710},[709],[586,3759],{"className":3760,"style":734},[733],[586,3762,3763,3766],{"style":737},[586,3764],{"className":3765,"style":710},[709],[586,3767,3769],{"className":3768},[714,715,716,717],[586,3770,3772,3775,3778,3781,3784],{"className":3771},[657,717],[586,3773,3581],{"className":3774},[657,717],[586,3776,622],{"className":3777},[753,717],[586,3779,3610],{"className":3780},[657,717],[586,3782,622],{"className":3783},[753,717],[586,3785,3639],{"className":3786},[657,717],[586,3788,767],{"className":3789},[766],[586,3791,3793],{"className":3792},[697],[586,3794,3796],{"className":3795,"style":774},[701],[586,3797],{},[586,3799],{"className":3800},[780,685],[586,3802],{"className":3803,"style":663},[662],[586,3805,611],{"className":3806},[667],[586,3808],{"className":3809,"style":663},[662],[586,3811,3813,3816],{"className":3812},[648],[586,3814],{"className":3815,"style":2842},[652],[586,3817,3690],{"className":3818},[657],[586,3820,3822],{"className":3821},[1732],[586,3823,3825,3873],{"className":3824},[589],[586,3826,3828],{"className":3827},[593],[595,3829,3830],{"xmlns":597,"display":1741},[599,3831,3832,3870],{},[602,3833,3834,3836,3838,3858,3860,3865,3867],{},[605,3835,1156],{},[609,3837,611],{},[3028,3839,3840],{},[602,3841,3842,3844,3846,3849,3851,3854,3856],{},[632,3843,3690],{},[609,3845,3036],{},[632,3847,3848],{},"8",[609,3850,3036],{},[632,3852,3853],{},"7",[609,3855,3036],{},[632,3857,2960],{},[609,3859,611],{},[3028,3861,3862],{},[632,3863,3864],{},"7056",[609,3866,611],{},[632,3868,3869],{},"84",[636,3871,3872],{"encoding":638},"A = \\sqrt{21 \\cdot 8 \\cdot 7 \\cdot 6} = \\sqrt{7056} = 84",[586,3874,3876,3894,3992,4054],{"className":3875,"ariaHidden":644},[643],[586,3877,3879,3882,3885,3888,3891],{"className":3878},[648],[586,3880],{"className":3881,"style":1191},[652],[586,3883,1156],{"className":3884},[657,658],[586,3886],{"className":3887,"style":663},[662],[586,3889,611],{"className":3890},[667],[586,3892],{"className":3893,"style":663},[662],[586,3895,3897,3900,3983,3986,3989],{"className":3896},[648],[586,3898],{"className":3899,"style":3112},[652],[586,3901,3903],{"className":3902},[657,3116],[586,3904,3906,3975],{"className":3905},[692,693],[586,3907,3909,3972],{"className":3908},[697],[586,3910,3912,3960],{"className":3911,"style":3126},[701],[586,3913,3915,3918],{"className":3914,"style":3131},[3130],[586,3916],{"className":3917,"style":710},[709],[586,3919,3921,3924,3927,3930,3933,3936,3939,3942,3945,3948,3951,3954,3957],{"className":3920,"style":3138},[657],[586,3922,3690],{"className":3923},[657],[586,3925],{"className":3926,"style":823},[662],[586,3928,3036],{"className":3929},[753],[586,3931],{"className":3932,"style":823},[662],[586,3934,3848],{"className":3935},[657],[586,3937],{"className":3938,"style":823},[662],[586,3940,3036],{"className":3941},[753],[586,3943],{"className":3944,"style":823},[662],[586,3946,3853],{"className":3947},[657],[586,3949],{"className":3950,"style":823},[662],[586,3952,3036],{"className":3953},[753],[586,3955],{"className":3956,"style":823},[662],[586,3958,2960],{"className":3959},[657],[586,3961,3962,3965],{"style":3180},[586,3963],{"className":3964,"style":710},[709],[586,3966,3968],{"className":3967,"style":3188},[3187],[3190,3969,3970],{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},[3198,3971],{"d":3200},[586,3973,767],{"className":3974},[766],[586,3976,3978],{"className":3977},[697],[586,3979,3981],{"className":3980,"style":3210},[701],[586,3982],{},[586,3984],{"className":3985,"style":663},[662],[586,3987,611],{"className":3988},[667],[586,3990],{"className":3991,"style":663},[662],[586,3993,3995,3998,4045,4048,4051],{"className":3994},[648],[586,3996],{"className":3997,"style":3112},[652],[586,3999,4001],{"className":4000},[657,3116],[586,4002,4004,4037],{"className":4003},[692,693],[586,4005,4007,4034],{"className":4006},[697],[586,4008,4010,4022],{"className":4009,"style":3126},[701],[586,4011,4013,4016],{"className":4012,"style":3131},[3130],[586,4014],{"className":4015,"style":710},[709],[586,4017,4019],{"className":4018,"style":3138},[657],[586,4020,3864],{"className":4021},[657],[586,4023,4024,4027],{"style":3180},[586,4025],{"className":4026,"style":710},[709],[586,4028,4030],{"className":4029,"style":3188},[3187],[3190,4031,4032],{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},[3198,4033],{"d":3200},[586,4035,767],{"className":4036},[766],[586,4038,4040],{"className":4039},[697],[586,4041,4043],{"className":4042,"style":3210},[701],[586,4044],{},[586,4046],{"className":4047,"style":663},[662],[586,4049,611],{"className":4050},[667],[586,4052],{"className":4053,"style":663},[662],[586,4055,4057,4060],{"className":4056},[648],[586,4058],{"className":4059,"style":2842},[652],[586,4061,3869],{"className":4062},[657],[564,4064,2807,4065,839,4108,892,4150,2941,4192,3007],{},[586,4066,4068,4087],{"className":4067},[589],[586,4069,4071],{"className":4070},[593],[595,4072,4073],{"xmlns":597},[599,4074,4075,4084],{},[602,4076,4077,4079,4081],{},[632,4078,2912],{},[2824,4080,2826],{},[2824,4082,4083],{},"m",[636,4085,4086],{"encoding":638},"5\\,\\text{m}",[586,4088,4090],{"className":4089,"ariaHidden":644},[643],[586,4091,4093,4096,4099,4102],{"className":4092},[648],[586,4094],{"className":4095,"style":2842},[652],[586,4097,2912],{"className":4098},[657],[586,4100],{"className":4101,"style":1287},[662],[586,4103,4105],{"className":4104},[657,2852],[586,4106,4083],{"className":4107},[657],[586,4109,4111,4129],{"className":4110},[589],[586,4112,4114],{"className":4113},[593],[595,4115,4116],{"xmlns":597},[599,4117,4118,4126],{},[602,4119,4120,4122,4124],{},[632,4121,2960],{},[2824,4123,2826],{},[2824,4125,4083],{},[636,4127,4128],{"encoding":638},"6\\,\\text{m}",[586,4130,4132],{"className":4131,"ariaHidden":644},[643],[586,4133,4135,4138,4141,4144],{"className":4134},[648],[586,4136],{"className":4137,"style":2842},[652],[586,4139,2960],{"className":4140},[657],[586,4142],{"className":4143,"style":1287},[662],[586,4145,4147],{"className":4146},[657,2852],[586,4148,4083],{"className":4149},[657],[586,4151,4153,4171],{"className":4152},[589],[586,4154,4156],{"className":4155},[593],[595,4157,4158],{"xmlns":597},[599,4159,4160,4168],{},[602,4161,4162,4164,4166],{},[632,4163,3853],{},[2824,4165,2826],{},[2824,4167,4083],{},[636,4169,4170],{"encoding":638},"7\\,\\text{m}",[586,4172,4174],{"className":4173,"ariaHidden":644},[643],[586,4175,4177,4180,4183,4186],{"className":4176},[648],[586,4178],{"className":4179,"style":2842},[652],[586,4181,3853],{"className":4182},[657],[586,4184],{"className":4185,"style":1287},[662],[586,4187,4189],{"className":4188},[657,2852],[586,4190,4083],{"className":4191},[657],[586,4193,4195,4218],{"className":4194},[589],[586,4196,4198],{"className":4197},[593],[595,4199,4200],{"xmlns":597},[599,4201,4202,4215],{},[602,4203,4204,4206,4208,4211,4213],{},[605,4205,607],{},[609,4207,611],{},[632,4209,4210],{},"9",[2824,4212,2826],{},[2824,4214,4083],{},[636,4216,4217],{"encoding":638},"s = 9\\,\\text{m}",[586,4219,4221,4239],{"className":4220,"ariaHidden":644},[643],[586,4222,4224,4227,4230,4233,4236],{"className":4223},[648],[586,4225],{"className":4226,"style":653},[652],[586,4228,607],{"className":4229},[657,658],[586,4231],{"className":4232,"style":663},[662],[586,4234,611],{"className":4235},[667],[586,4237],{"className":4238,"style":663},[662],[586,4240,4242,4245,4248,4251],{"className":4241},[648],[586,4243],{"className":4244,"style":2842},[652],[586,4246,4210],{"className":4247},[657],[586,4249],{"className":4250,"style":1287},[662],[586,4252,4254],{"className":4253},[657,2852],[586,4255,4083],{"className":4256},[657],[586,4258,4260],{"className":4259},[1732],[586,4261,4263,4350],{"className":4262},[589],[586,4264,4266],{"className":4265},[593],[595,4267,4268],{"xmlns":597,"display":1741},[599,4269,4270,4347],{},[602,4271,4272,4274,4276,4294,4296,4302,4304,4309,4311,4317,4319,4321,4325,4327,4333,4336,4339,4341],{},[605,4273,1156],{},[609,4275,611],{},[3028,4277,4278],{},[602,4279,4280,4282,4284,4286,4288,4290,4292],{},[632,4281,4210],{},[609,4283,3036],{},[632,4285,1759],{},[609,4287,3036],{},[632,4289,2822],{},[609,4291,3036],{},[632,4293,634],{},[2824,4295,2826],{},[1326,4297,4298,4300],{},[2824,4299,4083],{},[632,4301,634],{},[609,4303,611],{},[3028,4305,4306],{},[632,4307,4308],{},"216",[2824,4310,2826],{},[1326,4312,4313,4315],{},[2824,4314,4083],{},[632,4316,634],{},[609,4318,611],{},[632,4320,2960],{},[3028,4322,4323],{},[632,4324,2960],{},[2824,4326,2826],{},[1326,4328,4329,4331],{},[2824,4330,4083],{},[632,4332,634],{},[609,4334,4335],{},"≈",[632,4337,4338],{},"14,70",[2824,4340,2826],{},[1326,4342,4343,4345],{},[2824,4344,4083],{},[632,4346,634],{},[636,4348,4349],{"encoding":638},"A = \\sqrt{9 \\cdot 4 \\cdot 3 \\cdot 2}\\,\\text{m}^2 = \\sqrt{216}\\,\\text{m}^2 = 6\\sqrt{6}\\,\\text{m}^2 \\approx 14{,}70\\,\\text{m}^2",[586,4351,4353,4371,4504,4601,4701],{"className":4352,"ariaHidden":644},[643],[586,4354,4356,4359,4362,4365,4368],{"className":4355},[648],[586,4357],{"className":4358,"style":1191},[652],[586,4360,1156],{"className":4361},[657,658],[586,4363],{"className":4364,"style":663},[662],[586,4366,611],{"className":4367},[667],[586,4369],{"className":4370,"style":663},[662],[586,4372,4374,4377,4460,4463,4495,4498,4501],{"className":4373},[648],[586,4375],{"className":4376,"style":3112},[652],[586,4378,4380],{"className":4379},[657,3116],[586,4381,4383,4452],{"className":4382},[692,693],[586,4384,4386,4449],{"className":4385},[697],[586,4387,4389,4437],{"className":4388,"style":3126},[701],[586,4390,4392,4395],{"className":4391,"style":3131},[3130],[586,4393],{"className":4394,"style":710},[709],[586,4396,4398,4401,4404,4407,4410,4413,4416,4419,4422,4425,4428,4431,4434],{"className":4397,"style":3138},[657],[586,4399,4210],{"className":4400},[657],[586,4402],{"className":4403,"style":823},[662],[586,4405,3036],{"className":4406},[753],[586,4408],{"className":4409,"style":823},[662],[586,4411,1759],{"className":4412},[657],[586,4414],{"className":4415,"style":823},[662],[586,4417,3036],{"className":4418},[753],[586,4420],{"className":4421,"style":823},[662],[586,4423,2822],{"className":4424},[657],[586,4426],{"className":4427,"style":823},[662],[586,4429,3036],{"className":4430},[753],[586,4432],{"className":4433,"style":823},[662],[586,4435,634],{"className":4436},[657],[586,4438,4439,4442],{"style":3180},[586,4440],{"className":4441,"style":710},[709],[586,4443,4445],{"className":4444,"style":3188},[3187],[3190,4446,4447],{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},[3198,4448],{"d":3200},[586,4450,767],{"className":4451},[766],[586,4453,4455],{"className":4454},[697],[586,4456,4458],{"className":4457,"style":3210},[701],[586,4459],{},[586,4461],{"className":4462,"style":1287},[662],[586,4464,4466,4472],{"className":4465},[657],[586,4467,4469],{"className":4468},[657,2852],[586,4470,4083],{"className":4471},[657],[586,4473,4475],{"className":4474},[1458],[586,4476,4478],{"className":4477},[692],[586,4479,4481],{"className":4480},[697],[586,4482,4484],{"className":4483,"style":1820},[701],[586,4485,4486,4489],{"style":1844},[586,4487],{"className":4488,"style":1643},[709],[586,4490,4492],{"className":4491},[714,715,716,717],[586,4493,634],{"className":4494},[657,717],[586,4496],{"className":4497,"style":663},[662],[586,4499,611],{"className":4500},[667],[586,4502],{"className":4503,"style":663},[662],[586,4505,4507,4510,4557,4560,4592,4595,4598],{"className":4506},[648],[586,4508],{"className":4509,"style":3112},[652],[586,4511,4513],{"className":4512},[657,3116],[586,4514,4516,4549],{"className":4515},[692,693],[586,4517,4519,4546],{"className":4518},[697],[586,4520,4522,4534],{"className":4521,"style":3126},[701],[586,4523,4525,4528],{"className":4524,"style":3131},[3130],[586,4526],{"className":4527,"style":710},[709],[586,4529,4531],{"className":4530,"style":3138},[657],[586,4532,4308],{"className":4533},[657],[586,4535,4536,4539],{"style":3180},[586,4537],{"className":4538,"style":710},[709],[586,4540,4542],{"className":4541,"style":3188},[3187],[3190,4543,4544],{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},[3198,4545],{"d":3200},[586,4547,767],{"className":4548},[766],[586,4550,4552],{"className":4551},[697],[586,4553,4555],{"className":4554,"style":3210},[701],[586,4556],{},[586,4558],{"className":4559,"style":1287},[662],[586,4561,4563,4569],{"className":4562},[657],[586,4564,4566],{"className":4565},[657,2852],[586,4567,4083],{"className":4568},[657],[586,4570,4572],{"className":4571},[1458],[586,4573,4575],{"className":4574},[692],[586,4576,4578],{"className":4577},[697],[586,4579,4581],{"className":4580,"style":1820},[701],[586,4582,4583,4586],{"style":1844},[586,4584],{"className":4585,"style":1643},[709],[586,4587,4589],{"className":4588},[714,715,716,717],[586,4590,634],{"className":4591},[657,717],[586,4593],{"className":4594,"style":663},[662],[586,4596,611],{"className":4597},[667],[586,4599],{"className":4600,"style":663},[662],[586,4602,4604,4607,4610,4657,4660,4692,4695,4698],{"className":4603},[648],[586,4605],{"className":4606,"style":3112},[652],[586,4608,2960],{"className":4609},[657],[586,4611,4613],{"className":4612},[657,3116],[586,4614,4616,4649],{"className":4615},[692,693],[586,4617,4619,4646],{"className":4618},[697],[586,4620,4622,4634],{"className":4621,"style":3126},[701],[586,4623,4625,4628],{"className":4624,"style":3131},[3130],[586,4626],{"className":4627,"style":710},[709],[586,4629,4631],{"className":4630,"style":3138},[657],[586,4632,2960],{"className":4633},[657],[586,4635,4636,4639],{"style":3180},[586,4637],{"className":4638,"style":710},[709],[586,4640,4642],{"className":4641,"style":3188},[3187],[3190,4643,4644],{"xmlns":3192,"width":3193,"height":3194,"viewBox":3195,"preserveAspectRatio":3196},[3198,4645],{"d":3200},[586,4647,767],{"className":4648},[766],[586,4650,4652],{"className":4651},[697],[586,4653,4655],{"className":4654,"style":3210},[701],[586,4656],{},[586,4658],{"className":4659,"style":1287},[662],[586,4661,4663,4669],{"className":4662},[657],[586,4664,4666],{"className":4665},[657,2852],[586,4667,4083],{"className":4668},[657],[586,4670,4672],{"className":4671},[1458],[586,4673,4675],{"className":4674},[692],[586,4676,4678],{"className":4677},[697],[586,4679,4681],{"className":4680,"style":1820},[701],[586,4682,4683,4686],{"style":1844},[586,4684],{"className":4685,"style":1643},[709],[586,4687,4689],{"className":4688},[714,715,716,717],[586,4690,634],{"className":4691},[657,717],[586,4693],{"className":4694,"style":663},[662],[586,4696,4335],{"className":4697},[667],[586,4699],{"className":4700,"style":663},[662],[586,4702,4704,4708,4711,4719,4723,4726],{"className":4703},[648],[586,4705],{"className":4706,"style":4707},[652],"height:1.0585em;vertical-align:-0.1944em;",[586,4709,3610],{"className":4710},[657],[586,4712,4714],{"className":4713},[657],[586,4715,4718],{"className":4716},[4717],"mpunct",",",[586,4720,4722],{"className":4721},[657],"70",[586,4724],{"className":4725,"style":1287},[662],[586,4727,4729,4735],{"className":4728},[657],[586,4730,4732],{"className":4731},[657,2852],[586,4733,4083],{"className":4734},[657],[586,4736,4738],{"className":4737},[1458],[586,4739,4741],{"className":4740},[692],[586,4742,4744],{"className":4743},[697],[586,4745,4747],{"className":4746,"style":1820},[701],[586,4748,4749,4752],{"style":1844},[586,4750],{"className":4751,"style":1643},[709],[586,4753,4755],{"className":4754},[714,715,716,717],[586,4756,634],{"className":4757},[657,717],[559,4759,4761],{"id":4760},"typische-fehler","Typische Fehler",[4763,4764,4765,4768,4831],"ul",{},[578,4766,4767],{},"Mit dem ganzen Umfang statt dem halben rechnen.",[578,4769,4770,4771,4830],{},"Die Wurzel vergessen und ",[586,4772,4774,4792],{"className":4773},[589],[586,4775,4777],{"className":4776},[593],[595,4778,4779],{"xmlns":597},[599,4780,4781,4789],{},[602,4782,4783],{},[1326,4784,4785,4787],{},[605,4786,1156],{},[632,4788,634],{},[636,4790,4791],{"encoding":638},"A^2",[586,4793,4795],{"className":4794,"ariaHidden":644},[643],[586,4796,4798,4801],{"className":4797},[648],[586,4799],{"className":4800,"style":1709},[652],[586,4802,4804,4807],{"className":4803},[657],[586,4805,1156],{"className":4806},[657,658],[586,4808,4810],{"className":4809},[1458],[586,4811,4813],{"className":4812},[692],[586,4814,4816],{"className":4815},[697],[586,4817,4819],{"className":4818,"style":1709},[701],[586,4820,4821,4824],{"style":1712},[586,4822],{"className":4823,"style":1643},[709],[586,4825,4827],{"className":4826},[714,715,716,717],[586,4828,634],{"className":4829},[657,717]," als Ergebnis angeben.",[578,4832,4833,4834,839,4885,839,4936,4987,4988,5132],{},"Die Dreiecksungleichung nicht prüfen. Mit ",[586,4835,4837,4855],{"className":4836},[589],[586,4838,4840],{"className":4839},[593],[595,4841,4842],{"xmlns":597},[599,4843,4844,4852],{},[602,4845,4846,4848,4850],{},[605,4847,619],{},[609,4849,611],{},[632,4851,634],{},[636,4853,4854],{"encoding":638},"a = 2",[586,4856,4858,4876],{"className":4857,"ariaHidden":644},[643],[586,4859,4861,4864,4867,4870,4873],{"className":4860},[648],[586,4862],{"className":4863,"style":653},[652],[586,4865,619],{"className":4866},[657,658],[586,4868],{"className":4869,"style":663},[662],[586,4871,611],{"className":4872},[667],[586,4874],{"className":4875,"style":663},[662],[586,4877,4879,4882],{"className":4878},[648],[586,4880],{"className":4881,"style":2842},[652],[586,4883,634],{"className":4884},[657],[586,4886,4888,4906],{"className":4887},[589],[586,4889,4891],{"className":4890},[593],[595,4892,4893],{"xmlns":597},[599,4894,4895,4903],{},[602,4896,4897,4899,4901],{},[605,4898,625],{},[609,4900,611],{},[632,4902,2822],{},[636,4904,4905],{"encoding":638},"b = 3",[586,4907,4909,4927],{"className":4908,"ariaHidden":644},[643],[586,4910,4912,4915,4918,4921,4924],{"className":4911},[648],[586,4913],{"className":4914,"style":888},[652],[586,4916,625],{"className":4917},[657,658],[586,4919],{"className":4920,"style":663},[662],[586,4922,611],{"className":4923},[667],[586,4925],{"className":4926,"style":663},[662],[586,4928,4930,4933],{"className":4929},[648],[586,4931],{"className":4932,"style":2842},[652],[586,4934,2822],{"className":4935},[657],[586,4937,4939,4957],{"className":4938},[589],[586,4940,4942],{"className":4941},[593],[595,4943,4944],{"xmlns":597},[599,4945,4946,4954],{},[602,4947,4948,4950,4952],{},[605,4949,630],{},[609,4951,611],{},[632,4953,2960],{},[636,4955,4956],{"encoding":638},"c = 6",[586,4958,4960,4978],{"className":4959,"ariaHidden":644},[643],[586,4961,4963,4966,4969,4972,4975],{"className":4962},[648],[586,4964],{"className":4965,"style":653},[652],[586,4967,630],{"className":4968},[657,658],[586,4970],{"className":4971,"style":663},[662],[586,4973,611],{"className":4974},[667],[586,4976],{"className":4977,"style":663},[662],[586,4979,4981,4984],{"className":4980},[648],[586,4982],{"className":4983,"style":2842},[652],[586,4985,2960],{"className":4986},[657]," ist ",[586,4989,4991,5025],{"className":4990},[589],[586,4992,4994],{"className":4993},[593],[595,4995,4996],{"xmlns":597},[599,4997,4998,5022],{},[602,4999,5000,5002,5004,5006,5008,5011,5013,5015,5017,5019],{},[605,5001,607],{},[609,5003,801],{},[605,5005,630],{},[609,5007,611],{},[632,5009,5010],{},"5,5",[609,5012,801],{},[632,5014,2960],{},[609,5016,611],{},[609,5018,801],{},[632,5020,5021],{},"0,5",[636,5023,5024],{"encoding":638},"s - c = 5{,}5 - 6 = -0{,}5",[586,5026,5028,5046,5064,5092,5110],{"className":5027,"ariaHidden":644},[643],[586,5029,5031,5034,5037,5040,5043],{"className":5030},[648],[586,5032],{"className":5033,"style":816},[652],[586,5035,607],{"className":5036},[657,658],[586,5038],{"className":5039,"style":823},[662],[586,5041,801],{"className":5042},[753],[586,5044],{"className":5045,"style":823},[662],[586,5047,5049,5052,5055,5058,5061],{"className":5048},[648],[586,5050],{"className":5051,"style":653},[652],[586,5053,630],{"className":5054},[657,658],[586,5056],{"className":5057,"style":663},[662],[586,5059,611],{"className":5060},[667],[586,5062],{"className":5063,"style":663},[662],[586,5065,5067,5071,5074,5080,5083,5086,5089],{"className":5066},[648],[586,5068],{"className":5069,"style":5070},[652],"height:0.8389em;vertical-align:-0.1944em;",[586,5072,2912],{"className":5073},[657],[586,5075,5077],{"className":5076},[657],[586,5078,4718],{"className":5079},[4717],[586,5081,2912],{"className":5082},[657],[586,5084],{"className":5085,"style":823},[662],[586,5087,801],{"className":5088},[753],[586,5090],{"className":5091,"style":823},[662],[586,5093,5095,5098,5101,5104,5107],{"className":5094},[648],[586,5096],{"className":5097,"style":2842},[652],[586,5099,2960],{"className":5100},[657],[586,5102],{"className":5103,"style":663},[662],[586,5105,611],{"className":5106},[667],[586,5108],{"className":5109,"style":663},[662],[586,5111,5113,5116,5119,5123,5129],{"className":5112},[648],[586,5114],{"className":5115,"style":5070},[652],[586,5117,801],{"className":5118},[657],[586,5120,5122],{"className":5121},[657],"0",[586,5124,5126],{"className":5125},[657],[586,5127,4718],{"className":5128},[4717],[586,5130,2912],{"className":5131},[657]," negativ: Diese Längen bilden kein Dreieck.",{"title":5134,"searchDepth":5135,"depth":5135,"links":5136},"",2,[5137,5138,5139,5140],{"id":561,"depth":5135,"text":562},{"id":1137,"depth":5135,"text":1138},{"id":2803,"depth":5135,"text":2804},{"id":4760,"depth":5135,"text":4761},[5142,5145,5148,5151,5153,5155,5158,5161],{"lhs":5143,"rhs":5144},"16 * ((a + b + c)\u002F2) * ((b + c - a)\u002F2) * ((a + c - b)\u002F2) * ((a + b - c)\u002F2)","2*a^2*b^2 + 2*b^2*c^2 + 2*c^2*a^2 - a^4 - b^4 - c^4",{"lhs":5146,"rhs":5147},"sqrt(3*a\u002F2 * (a\u002F2)^3)","a^2\u002F4*sqrt(3)",{"lhs":5149,"rhs":5150},"sqrt(6*(6 - 3)*(6 - 4)*(6 - 5))","1\u002F2*3*4",{"lhs":5152,"rhs":3690},"(13 + 14 + 15)\u002F2",{"lhs":5154,"rhs":3869},"sqrt(21*8*7*6)",{"lhs":5156,"rhs":5157},"sqrt(9*(9 - 5)*(9 - 6)*(9 - 7))","6*sqrt(6)",{"lhs":5159,"rhs":5160},"round(6*sqrt(6), 2)","14.7",{"lhs":5162,"rhs":5163},"(2 + 3 + 6)\u002F2 - 6","-0.5","a, b, c > 0,\\ a + b > c,\\ a + c > b,\\ b + c > a","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a + b > c,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a + c > b,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b + c > a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":5169,"x":5170,"y":5173,"items":5176},"Dreieck mit den drei Seitenlängen a, b und c",[5171,5172],-0.6,5.5,[5174,5175],-0.7,4.7,[5177,5188,5193,5197,5201,5207,5212],{"type":5178,"points":5179,"fill":5187},"polygon",[5180,5182,5184],[5181,5181],0,[5183,5181],4.9,[5185,5186],3.15,4.2,true,{"type":5189,"at":5190,"text":630},"label",[5191,5192],2.45,-0.35,{"type":5189,"at":5194,"text":619},[5195,5196],4.35,2.23,{"type":5189,"at":5198,"text":625},[5199,5200],1.3,2.31,{"type":5202,"at":5203,"label":1156,"offset":5204},"point",[5181,5181],[5205,5206],-18,4,{"type":5202,"at":5208,"label":5209,"offset":5210},[5183,5181],"B",[5211,5206],8,{"type":5202,"at":5213,"label":5214,"offset":5215},[5185,5186],"C",[5216,5217],-6,-14,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 292.8 259.2\" width=\"292.8\" height=\"259.2\" role=\"img\" aria-label=\"Dreieck mit den drei Seitenlängen a, b und c\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-heron-formula-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-heron-formula-clip\">\u003Crect x=\"0\" y=\"0\" width=\"292.8\" height=\"259.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"28.8,225.6 264,225.6 180,24\" class=\"fig-main fig-fill\"\u002F>\u003Ctext x=\"146.4\" y=\"242.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ctext x=\"237.6\" y=\"118.56\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"91.2\" y=\"114.72\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ccircle cx=\"28.8\" cy=\"225.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"10.8\" y=\"229.6\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"264\" cy=\"225.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"272\" y=\"229.6\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"180\" cy=\"24\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"174\" y=\"10\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003C\u002Fsvg>","heron-formula","\\begin{gathered} A = \\sqrt{s(s - a)(s - b)(s - c)} \\\\ s = \\frac{a + b + c}{2} \\end{gathered}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"center\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmi>s\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cannotation encoding=\"application\u002Fx-tex\">\\begin{gathered} A = \\sqrt{s(s - a)(s - b)(s - c)} \\\\ s = \\frac{a + b + c}{2} \\end{gathered}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:3.7013em;vertical-align:-1.6007em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.1007em;\">\u003Cspan style=\"top:-4.4882em;\">\u003Cspan class=\"pstrut\" style=\"height:3.3714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9839em;\">\u003Cspan class=\"svg-align\" style=\"top:-3.2em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:1em;\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9439em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2561em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.4568em;\">\u003Cspan class=\"pstrut\" style=\"height:3.3714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6007em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-heron",[],[5227,5228,5229,5230],"triangle-area","triangle-perimeter","law-of-cosines","triangle-area-sine",{"title":548,"description":5134},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-heron","Der Flächeninhalt eines Dreiecks lässt sich allein aus den drei Seitenlängen über den halben Umfang berechnen.",[5235,5236,5237,5238],"flächeninhalt","dreieck","heron","seitenlänge",[5240,5243,5247],{"symbol":1156,"meaning":5241,"symbolHtml":5242},"Flächeninhalt des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5244,"meaning":5245,"symbolHtml":5246},"a, b, c","die drei Seitenlängen des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":607,"meaning":5248,"symbolHtml":5249},"halber Umfang des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","_vfmvTOcFncUvizRDzXmUzUQyYfJWwHK6BcygDrCU-s",[5252,5255,5258,5261],{"stem":5253,"title":5254,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-dreieck","Flächeninhalt eines Dreiecks",{"stem":5256,"title":5257,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-dreieck","Umfang eines Dreiecks",{"stem":5259,"title":5260,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus","Flächeninhalt eines Dreiecks mit Sinus",{"stem":5262,"title":5263,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fkosinussatz","Kosinussatz",1793824269804]