[{"data":1,"prerenderedAt":2758},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-drachenviereck":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-drachenviereck":2748},[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":554,"category":247,"checks":2666,"conditions":2674,"conditionsHtml":2674,"deprecated":2674,"description":2659,"extension":2675,"figure":2676,"figureCaption":2677,"figureHtml":2720,"formulaId":2721,"latex":754,"latexHtml":2722,"level":2723,"meta":2724,"navigation":2697,"path":2725,"redirectFrom":2726,"related":2727,"seo":2731,"stem":2732,"subject":585,"summary":2733,"tags":2734,"variables":2739,"__hash__":2747},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-drachenviereck.md","Flächeninhalt eines Drachenvierecks",[550,551,552,553],"Drachen Flächeninhalt","Fläche Drachenviereck","A = e·f\u002F2","Drachenviereck Fläche berechnen",{"type":555,"value":556,"toc":2658},"minimark",[557,562,654,917,920,924,1043,1756,1760,1899,2129,2252,2527,2531],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,570,571,574,575,621,622,653],"p",{},"Ein ",[567,568,569],"strong",{},"Drachenviereck"," hat zwei Paare gleich langer Nachbarseiten, wie ein Papierdrachen. Seine beiden ",[567,572,573],{},"Diagonalen"," ",[576,577,580,602],"span",{"className":578},[579],"katex",[576,581,584],{"className":582},[583],"katex-mathml",[585,586,588],"math",{"xmlns":587},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[589,590,591,598],"semantics",{},[592,593,594],"mrow",{},[595,596,597],"mi",{},"e",[599,600,597],"annotation",{"encoding":601},"application\u002Fx-tex",[576,603,607],{"className":604,"ariaHidden":606},[605],"katex-html","true",[576,608,611,616],{"className":609},[610],"base",[576,612],{"className":613,"style":615},[614],"strut","height:0.4306em;",[576,617,597],{"className":618},[619,620],"mord","mathnormal"," und ",[576,623,625,639],{"className":624},[579],[576,626,628],{"className":627},[583],[585,629,630],{"xmlns":587},[589,631,632,637],{},[592,633,634],{},[595,635,636],{},"f",[599,638,636],{"encoding":601},[576,640,642],{"className":641,"ariaHidden":606},[605],[576,643,645,649],{"className":644},[610],[576,646],{"className":647,"style":648},[614],"height:0.8889em;vertical-align:-0.1944em;",[576,650,636],{"className":651,"style":652},[619,620],"margin-right:0.1076em;"," stehen senkrecht aufeinander.",[563,655,656,657,621,685,713,714,916],{},"Man kann sich ein Rechteck mit den Seiten ",[576,658,660,673],{"className":659},[579],[576,661,663],{"className":662},[583],[585,664,665],{"xmlns":587},[589,666,667,671],{},[592,668,669],{},[595,670,597],{},[599,672,597],{"encoding":601},[576,674,676],{"className":675,"ariaHidden":606},[605],[576,677,679,682],{"className":678},[610],[576,680],{"className":681,"style":615},[614],[576,683,597],{"className":684},[619,620],[576,686,688,701],{"className":687},[579],[576,689,691],{"className":690},[583],[585,692,693],{"xmlns":587},[589,694,695,699],{},[592,696,697],{},[595,698,636],{},[599,700,636],{"encoding":601},[576,702,704],{"className":703,"ariaHidden":606},[605],[576,705,707,710],{"className":706},[610],[576,708],{"className":709,"style":648},[614],[576,711,636],{"className":712,"style":652},[619,620]," um den Drachen legen. Der Drache füllt genau die Hälfte davon aus. Deshalb gilt ",[576,715,717,755],{"className":716},[579],[576,718,720],{"className":719},[583],[585,721,722],{"xmlns":587},[589,723,724,752],{},[592,725,726,729,733,743,746,748,750],{},[595,727,728],{},"A",[730,731,732],"mo",{},"=",[734,735,736,740],"mfrac",{},[737,738,739],"mn",{},"1",[737,741,742],{},"2",[730,744,745],{},"⋅",[595,747,597],{},[730,749,745],{},[595,751,636],{},[599,753,754],{"encoding":601},"A = \\frac{1}{2} \\cdot e \\cdot f",[576,756,758,780,888,907],{"className":757,"ariaHidden":606},[605],[576,759,761,765,768,773,777],{"className":760},[610],[576,762],{"className":763,"style":764},[614],"height:0.6833em;",[576,766,728],{"className":767},[619,620],[576,769],{"className":770,"style":772},[771],"mspace","margin-right:0.2778em;",[576,774,732],{"className":775},[776],"mrel",[576,778],{"className":779,"style":772},[771],[576,781,783,787,877,881,885],{"className":782},[610],[576,784],{"className":785,"style":786},[614],"height:1.1901em;vertical-align:-0.345em;",[576,788,790,795,873],{"className":789},[619],[576,791],{"className":792},[793,794],"mopen","nulldelimiter",[576,796,798],{"className":797},[734],[576,799,803,864],{"className":800},[801,802],"vlist-t","vlist-t2",[576,804,807,859],{"className":805},[806],"vlist-r",[576,808,812,833,844],{"className":809,"style":811},[810],"vlist","height:0.8451em;",[576,813,815,820],{"style":814},"top:-2.655em;",[576,816],{"className":817,"style":819},[818],"pstrut","height:3em;",[576,821,827],{"className":822},[823,824,825,826],"sizing","reset-size6","size3","mtight",[576,828,830],{"className":829},[619,826],[576,831,742],{"className":832},[619,826],[576,834,836,839],{"style":835},"top:-3.23em;",[576,837],{"className":838,"style":819},[818],[576,840],{"className":841,"style":843},[842],"frac-line","border-bottom-width:0.04em;",[576,845,847,850],{"style":846},"top:-3.394em;",[576,848],{"className":849,"style":819},[818],[576,851,853],{"className":852},[823,824,825,826],[576,854,856],{"className":855},[619,826],[576,857,739],{"className":858},[619,826],[576,860,863],{"className":861},[862],"vlist-s","​",[576,865,867],{"className":866},[806],[576,868,871],{"className":869,"style":870},[810],"height:0.345em;",[576,872],{},[576,874],{"className":875},[876,794],"mclose",[576,878],{"className":879,"style":880},[771],"margin-right:0.2222em;",[576,882,745],{"className":883},[884],"mbin",[576,886],{"className":887,"style":880},[771],[576,889,891,895,898,901,904],{"className":890},[610],[576,892],{"className":893,"style":894},[614],"height:0.4445em;",[576,896,597],{"className":897},[619,620],[576,899],{"className":900,"style":880},[771],[576,902,745],{"className":903},[884],[576,905],{"className":906,"style":880},[771],[576,908,910,913],{"className":909},[610],[576,911],{"className":912,"style":648},[614],[576,914,636],{"className":915,"style":652},[619,620],".",[563,918,919],{},"Die Formel gilt genauso für die Raute und das Quadrat, denn auch dort stehen die Diagonalen senkrecht aufeinander.",[558,921,923],{"id":922},"herleitung","Herleitung",[563,925,926,927,955,956,984,985,1013,1014,1042],{},"Die Diagonale ",[576,928,930,943],{"className":929},[579],[576,931,933],{"className":932},[583],[585,934,935],{"xmlns":587},[589,936,937,941],{},[592,938,939],{},[595,940,636],{},[599,942,636],{"encoding":601},[576,944,946],{"className":945,"ariaHidden":606},[605],[576,947,949,952],{"className":948},[610],[576,950],{"className":951,"style":648},[614],[576,953,636],{"className":954,"style":652},[619,620]," teilt den Drachen in zwei Dreiecke. Beide haben die Grundseite ",[576,957,959,972],{"className":958},[579],[576,960,962],{"className":961},[583],[585,963,964],{"xmlns":587},[589,965,966,970],{},[592,967,968],{},[595,969,636],{},[599,971,636],{"encoding":601},[576,973,975],{"className":974,"ariaHidden":606},[605],[576,976,978,981],{"className":977},[610],[576,979],{"className":980,"style":648},[614],[576,982,636],{"className":983,"style":652},[619,620],". Ihre Höhen sind die beiden Teilstücke der Diagonale ",[576,986,988,1001],{"className":987},[579],[576,989,991],{"className":990},[583],[585,992,993],{"xmlns":587},[589,994,995,999],{},[592,996,997],{},[595,998,597],{},[599,1000,597],{"encoding":601},[576,1002,1004],{"className":1003,"ariaHidden":606},[605],[576,1005,1007,1010],{"className":1006},[610],[576,1008],{"className":1009,"style":615},[614],[576,1011,597],{"className":1012},[619,620],", zusammen also ",[576,1015,1017,1030],{"className":1016},[579],[576,1018,1020],{"className":1019},[583],[585,1021,1022],{"xmlns":587},[589,1023,1024,1028],{},[592,1025,1026],{},[595,1027,597],{},[599,1029,597],{"encoding":601},[576,1031,1033],{"className":1032,"ariaHidden":606},[605],[576,1034,1036,1039],{"className":1035},[610],[576,1037],{"className":1038,"style":615},[614],[576,1040,597],{"className":1041},[619,620],":",[576,1044,1047],{"className":1045},[1046],"katex-display",[576,1048,1050,1152],{"className":1049},[579],[576,1051,1053],{"className":1052},[583],[585,1054,1056],{"xmlns":587,"display":1055},"block",[589,1057,1058,1149],{},[592,1059,1060,1062,1064,1070,1072,1074,1081,1084,1090,1092,1094,1100,1102,1108,1110,1112,1116,1122,1124,1130,1133,1135,1141,1143,1145,1147],{},[595,1061,728],{},[730,1063,732],{},[734,1065,1066,1068],{},[737,1067,739],{},[737,1069,742],{},[595,1071,636],{},[730,1073,745],{},[1075,1076,1077,1079],"msub",{},[595,1078,597],{},[737,1080,739],{},[730,1082,1083],{},"+",[734,1085,1086,1088],{},[737,1087,739],{},[737,1089,742],{},[595,1091,636],{},[730,1093,745],{},[1075,1095,1096,1098],{},[595,1097,597],{},[737,1099,742],{},[730,1101,732],{},[734,1103,1104,1106],{},[737,1105,739],{},[737,1107,742],{},[595,1109,636],{},[730,1111,745],{},[730,1113,1115],{"stretchy":1114},"false","(",[1075,1117,1118,1120],{},[595,1119,597],{},[737,1121,739],{},[730,1123,1083],{},[1075,1125,1126,1128],{},[595,1127,597],{},[737,1129,742],{},[730,1131,1132],{"stretchy":1114},")",[730,1134,732],{},[734,1136,1137,1139],{},[737,1138,739],{},[737,1140,742],{},[730,1142,745],{},[595,1144,597],{},[730,1146,745],{},[595,1148,636],{},[599,1150,1151],{"encoding":601},"A = \\frac{1}{2} f \\cdot e_1 + \\frac{1}{2} f \\cdot e_2 = \\frac{1}{2} f \\cdot (e_1 + e_2) = \\frac{1}{2} \\cdot e \\cdot f",[576,1153,1155,1173,1258,1319,1399,1455,1535,1594,1652,1729,1747],{"className":1154,"ariaHidden":606},[605],[576,1156,1158,1161,1164,1167,1170],{"className":1157},[610],[576,1159],{"className":1160,"style":764},[614],[576,1162,728],{"className":1163},[619,620],[576,1165],{"className":1166,"style":772},[771],[576,1168,732],{"className":1169},[776],[576,1171],{"className":1172,"style":772},[771],[576,1174,1176,1180,1246,1249,1252,1255],{"className":1175},[610],[576,1177],{"className":1178,"style":1179},[614],"height:2.0074em;vertical-align:-0.686em;",[576,1181,1183,1186,1243],{"className":1182},[619],[576,1184],{"className":1185},[793,794],[576,1187,1189],{"className":1188},[734],[576,1190,1192,1234],{"className":1191},[801,802],[576,1193,1195,1231],{"className":1194},[806],[576,1196,1199,1211,1219],{"className":1197,"style":1198},[810],"height:1.3214em;",[576,1200,1202,1205],{"style":1201},"top:-2.314em;",[576,1203],{"className":1204,"style":819},[818],[576,1206,1208],{"className":1207},[619],[576,1209,742],{"className":1210},[619],[576,1212,1213,1216],{"style":835},[576,1214],{"className":1215,"style":819},[818],[576,1217],{"className":1218,"style":843},[842],[576,1220,1222,1225],{"style":1221},"top:-3.677em;",[576,1223],{"className":1224,"style":819},[818],[576,1226,1228],{"className":1227},[619],[576,1229,739],{"className":1230},[619],[576,1232,863],{"className":1233},[862],[576,1235,1237],{"className":1236},[806],[576,1238,1241],{"className":1239,"style":1240},[810],"height:0.686em;",[576,1242],{},[576,1244],{"className":1245},[876,794],[576,1247,636],{"className":1248,"style":652},[619,620],[576,1250],{"className":1251,"style":880},[771],[576,1253,745],{"className":1254},[884],[576,1256],{"className":1257,"style":880},[771],[576,1259,1261,1265,1310,1313,1316],{"className":1260},[610],[576,1262],{"className":1263,"style":1264},[614],"height:0.7333em;vertical-align:-0.15em;",[576,1266,1268,1271],{"className":1267},[619],[576,1269,597],{"className":1270},[619,620],[576,1272,1275],{"className":1273},[1274],"msupsub",[576,1276,1278,1301],{"className":1277},[801,802],[576,1279,1281,1298],{"className":1280},[806],[576,1282,1285],{"className":1283,"style":1284},[810],"height:0.3011em;",[576,1286,1288,1292],{"style":1287},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[576,1289],{"className":1290,"style":1291},[818],"height:2.7em;",[576,1293,1295],{"className":1294},[823,824,825,826],[576,1296,739],{"className":1297},[619,826],[576,1299,863],{"className":1300},[862],[576,1302,1304],{"className":1303},[806],[576,1305,1308],{"className":1306,"style":1307},[810],"height:0.15em;",[576,1309],{},[576,1311],{"className":1312,"style":880},[771],[576,1314,1083],{"className":1315},[884],[576,1317],{"className":1318,"style":880},[771],[576,1320,1322,1325,1387,1390,1393,1396],{"className":1321},[610],[576,1323],{"className":1324,"style":1179},[614],[576,1326,1328,1331,1384],{"className":1327},[619],[576,1329],{"className":1330},[793,794],[576,1332,1334],{"className":1333},[734],[576,1335,1337,1376],{"className":1336},[801,802],[576,1338,1340,1373],{"className":1339},[806],[576,1341,1343,1354,1362],{"className":1342,"style":1198},[810],[576,1344,1345,1348],{"style":1201},[576,1346],{"className":1347,"style":819},[818],[576,1349,1351],{"className":1350},[619],[576,1352,742],{"className":1353},[619],[576,1355,1356,1359],{"style":835},[576,1357],{"className":1358,"style":819},[818],[576,1360],{"className":1361,"style":843},[842],[576,1363,1364,1367],{"style":1221},[576,1365],{"className":1366,"style":819},[818],[576,1368,1370],{"className":1369},[619],[576,1371,739],{"className":1372},[619],[576,1374,863],{"className":1375},[862],[576,1377,1379],{"className":1378},[806],[576,1380,1382],{"className":1381,"style":1240},[810],[576,1383],{},[576,1385],{"className":1386},[876,794],[576,1388,636],{"className":1389,"style":652},[619,620],[576,1391],{"className":1392,"style":880},[771],[576,1394,745],{"className":1395},[884],[576,1397],{"className":1398,"style":880},[771],[576,1400,1402,1406,1446,1449,1452],{"className":1401},[610],[576,1403],{"className":1404,"style":1405},[614],"height:0.5806em;vertical-align:-0.15em;",[576,1407,1409,1412],{"className":1408},[619],[576,1410,597],{"className":1411},[619,620],[576,1413,1415],{"className":1414},[1274],[576,1416,1418,1438],{"className":1417},[801,802],[576,1419,1421,1435],{"className":1420},[806],[576,1422,1424],{"className":1423,"style":1284},[810],[576,1425,1426,1429],{"style":1287},[576,1427],{"className":1428,"style":1291},[818],[576,1430,1432],{"className":1431},[823,824,825,826],[576,1433,742],{"className":1434},[619,826],[576,1436,863],{"className":1437},[862],[576,1439,1441],{"className":1440},[806],[576,1442,1444],{"className":1443,"style":1307},[810],[576,1445],{},[576,1447],{"className":1448,"style":772},[771],[576,1450,732],{"className":1451},[776],[576,1453],{"className":1454,"style":772},[771],[576,1456,1458,1461,1523,1526,1529,1532],{"className":1457},[610],[576,1459],{"className":1460,"style":1179},[614],[576,1462,1464,1467,1520],{"className":1463},[619],[576,1465],{"className":1466},[793,794],[576,1468,1470],{"className":1469},[734],[576,1471,1473,1512],{"className":1472},[801,802],[576,1474,1476,1509],{"className":1475},[806],[576,1477,1479,1490,1498],{"className":1478,"style":1198},[810],[576,1480,1481,1484],{"style":1201},[576,1482],{"className":1483,"style":819},[818],[576,1485,1487],{"className":1486},[619],[576,1488,742],{"className":1489},[619],[576,1491,1492,1495],{"style":835},[576,1493],{"className":1494,"style":819},[818],[576,1496],{"className":1497,"style":843},[842],[576,1499,1500,1503],{"style":1221},[576,1501],{"className":1502,"style":819},[818],[576,1504,1506],{"className":1505},[619],[576,1507,739],{"className":1508},[619],[576,1510,863],{"className":1511},[862],[576,1513,1515],{"className":1514},[806],[576,1516,1518],{"className":1517,"style":1240},[810],[576,1519],{},[576,1521],{"className":1522},[876,794],[576,1524,636],{"className":1525,"style":652},[619,620],[576,1527],{"className":1528,"style":880},[771],[576,1530,745],{"className":1531},[884],[576,1533],{"className":1534,"style":880},[771],[576,1536,1538,1542,1545,1585,1588,1591],{"className":1537},[610],[576,1539],{"className":1540,"style":1541},[614],"height:1em;vertical-align:-0.25em;",[576,1543,1115],{"className":1544},[793],[576,1546,1548,1551],{"className":1547},[619],[576,1549,597],{"className":1550},[619,620],[576,1552,1554],{"className":1553},[1274],[576,1555,1557,1577],{"className":1556},[801,802],[576,1558,1560,1574],{"className":1559},[806],[576,1561,1563],{"className":1562,"style":1284},[810],[576,1564,1565,1568],{"style":1287},[576,1566],{"className":1567,"style":1291},[818],[576,1569,1571],{"className":1570},[823,824,825,826],[576,1572,739],{"className":1573},[619,826],[576,1575,863],{"className":1576},[862],[576,1578,1580],{"className":1579},[806],[576,1581,1583],{"className":1582,"style":1307},[810],[576,1584],{},[576,1586],{"className":1587,"style":880},[771],[576,1589,1083],{"className":1590},[884],[576,1592],{"className":1593,"style":880},[771],[576,1595,1597,1600,1640,1643,1646,1649],{"className":1596},[610],[576,1598],{"className":1599,"style":1541},[614],[576,1601,1603,1606],{"className":1602},[619],[576,1604,597],{"className":1605},[619,620],[576,1607,1609],{"className":1608},[1274],[576,1610,1612,1632],{"className":1611},[801,802],[576,1613,1615,1629],{"className":1614},[806],[576,1616,1618],{"className":1617,"style":1284},[810],[576,1619,1620,1623],{"style":1287},[576,1621],{"className":1622,"style":1291},[818],[576,1624,1626],{"className":1625},[823,824,825,826],[576,1627,742],{"className":1628},[619,826],[576,1630,863],{"className":1631},[862],[576,1633,1635],{"className":1634},[806],[576,1636,1638],{"className":1637,"style":1307},[810],[576,1639],{},[576,1641,1132],{"className":1642},[876],[576,1644],{"className":1645,"style":772},[771],[576,1647,732],{"className":1648},[776],[576,1650],{"className":1651,"style":772},[771],[576,1653,1655,1658,1720,1723,1726],{"className":1654},[610],[576,1656],{"className":1657,"style":1179},[614],[576,1659,1661,1664,1717],{"className":1660},[619],[576,1662],{"className":1663},[793,794],[576,1665,1667],{"className":1666},[734],[576,1668,1670,1709],{"className":1669},[801,802],[576,1671,1673,1706],{"className":1672},[806],[576,1674,1676,1687,1695],{"className":1675,"style":1198},[810],[576,1677,1678,1681],{"style":1201},[576,1679],{"className":1680,"style":819},[818],[576,1682,1684],{"className":1683},[619],[576,1685,742],{"className":1686},[619],[576,1688,1689,1692],{"style":835},[576,1690],{"className":1691,"style":819},[818],[576,1693],{"className":1694,"style":843},[842],[576,1696,1697,1700],{"style":1221},[576,1698],{"className":1699,"style":819},[818],[576,1701,1703],{"className":1702},[619],[576,1704,739],{"className":1705},[619],[576,1707,863],{"className":1708},[862],[576,1710,1712],{"className":1711},[806],[576,1713,1715],{"className":1714,"style":1240},[810],[576,1716],{},[576,1718],{"className":1719},[876,794],[576,1721],{"className":1722,"style":880},[771],[576,1724,745],{"className":1725},[884],[576,1727],{"className":1728,"style":880},[771],[576,1730,1732,1735,1738,1741,1744],{"className":1731},[610],[576,1733],{"className":1734,"style":894},[614],[576,1736,597],{"className":1737},[619,620],[576,1739],{"className":1740,"style":880},[771],[576,1742,745],{"className":1743},[884],[576,1745],{"className":1746,"style":880},[771],[576,1748,1750,1753],{"className":1749},[610],[576,1751],{"className":1752,"style":648},[614],[576,1754,636],{"className":1755,"style":652},[619,620],[558,1757,1759],{"id":1758},"beispiele","Beispiele",[563,1761,1762,1763,621,1834,1042],{},"Ein Drachen hat die Diagonalen ",[576,1764,1766,1792],{"className":1765},[579],[576,1767,1769],{"className":1768},[583],[585,1770,1771],{"xmlns":587},[589,1772,1773,1789],{},[592,1774,1775,1777,1779,1782,1786],{},[595,1776,597],{},[730,1778,732],{},[737,1780,1781],{},"6",[1783,1784,1785],"mtext",{}," ",[1783,1787,1788],{},"cm",[599,1790,1791],{"encoding":601},"e = 6\\,\\text{cm}",[576,1793,1795,1813],{"className":1794,"ariaHidden":606},[605],[576,1796,1798,1801,1804,1807,1810],{"className":1797},[610],[576,1799],{"className":1800,"style":615},[614],[576,1802,597],{"className":1803},[619,620],[576,1805],{"className":1806,"style":772},[771],[576,1808,732],{"className":1809},[776],[576,1811],{"className":1812,"style":772},[771],[576,1814,1816,1820,1823,1827],{"className":1815},[610],[576,1817],{"className":1818,"style":1819},[614],"height:0.6444em;",[576,1821,1781],{"className":1822},[619],[576,1824],{"className":1825,"style":1826},[771],"margin-right:0.1667em;",[576,1828,1831],{"className":1829},[619,1830],"text",[576,1832,1788],{"className":1833},[619],[576,1835,1837,1860],{"className":1836},[579],[576,1838,1840],{"className":1839},[583],[585,1841,1842],{"xmlns":587},[589,1843,1844,1857],{},[592,1845,1846,1848,1850,1853,1855],{},[595,1847,636],{},[730,1849,732],{},[737,1851,1852],{},"10",[1783,1854,1785],{},[1783,1856,1788],{},[599,1858,1859],{"encoding":601},"f = 10\\,\\text{cm}",[576,1861,1863,1881],{"className":1862,"ariaHidden":606},[605],[576,1864,1866,1869,1872,1875,1878],{"className":1865},[610],[576,1867],{"className":1868,"style":648},[614],[576,1870,636],{"className":1871,"style":652},[619,620],[576,1873],{"className":1874,"style":772},[771],[576,1876,732],{"className":1877},[776],[576,1879],{"className":1880,"style":772},[771],[576,1882,1884,1887,1890,1893],{"className":1883},[610],[576,1885],{"className":1886,"style":1819},[614],[576,1888,1852],{"className":1889},[619],[576,1891],{"className":1892,"style":1826},[771],[576,1894,1896],{"className":1895},[619,1830],[576,1897,1788],{"className":1898},[619],[576,1900,1902],{"className":1901},[1046],[576,1903,1905,1949],{"className":1904},[579],[576,1906,1908],{"className":1907},[583],[585,1909,1910],{"xmlns":587,"display":1055},[589,1911,1912,1946],{},[592,1913,1914,1916,1918,1924,1926,1928,1930,1932,1934,1937,1939],{},[595,1915,728],{},[730,1917,732],{},[734,1919,1920,1922],{},[737,1921,739],{},[737,1923,742],{},[730,1925,745],{},[737,1927,1781],{},[730,1929,745],{},[737,1931,1852],{},[730,1933,732],{},[737,1935,1936],{},"30",[1783,1938,1785],{},[1940,1941,1942,1944],"msup",{},[1783,1943,1788],{},[737,1945,742],{},[599,1947,1948],{"encoding":601},"A = \\frac{1}{2} \\cdot 6 \\cdot 10 = 30\\,\\text{cm}^2",[576,1950,1952,1970,2047,2065,2083],{"className":1951,"ariaHidden":606},[605],[576,1953,1955,1958,1961,1964,1967],{"className":1954},[610],[576,1956],{"className":1957,"style":764},[614],[576,1959,728],{"className":1960},[619,620],[576,1962],{"className":1963,"style":772},[771],[576,1965,732],{"className":1966},[776],[576,1968],{"className":1969,"style":772},[771],[576,1971,1973,1976,2038,2041,2044],{"className":1972},[610],[576,1974],{"className":1975,"style":1179},[614],[576,1977,1979,1982,2035],{"className":1978},[619],[576,1980],{"className":1981},[793,794],[576,1983,1985],{"className":1984},[734],[576,1986,1988,2027],{"className":1987},[801,802],[576,1989,1991,2024],{"className":1990},[806],[576,1992,1994,2005,2013],{"className":1993,"style":1198},[810],[576,1995,1996,1999],{"style":1201},[576,1997],{"className":1998,"style":819},[818],[576,2000,2002],{"className":2001},[619],[576,2003,742],{"className":2004},[619],[576,2006,2007,2010],{"style":835},[576,2008],{"className":2009,"style":819},[818],[576,2011],{"className":2012,"style":843},[842],[576,2014,2015,2018],{"style":1221},[576,2016],{"className":2017,"style":819},[818],[576,2019,2021],{"className":2020},[619],[576,2022,739],{"className":2023},[619],[576,2025,863],{"className":2026},[862],[576,2028,2030],{"className":2029},[806],[576,2031,2033],{"className":2032,"style":1240},[810],[576,2034],{},[576,2036],{"className":2037},[876,794],[576,2039],{"className":2040,"style":880},[771],[576,2042,745],{"className":2043},[884],[576,2045],{"className":2046,"style":880},[771],[576,2048,2050,2053,2056,2059,2062],{"className":2049},[610],[576,2051],{"className":2052,"style":1819},[614],[576,2054,1781],{"className":2055},[619],[576,2057],{"className":2058,"style":880},[771],[576,2060,745],{"className":2061},[884],[576,2063],{"className":2064,"style":880},[771],[576,2066,2068,2071,2074,2077,2080],{"className":2067},[610],[576,2069],{"className":2070,"style":1819},[614],[576,2072,1852],{"className":2073},[619],[576,2075],{"className":2076,"style":772},[771],[576,2078,732],{"className":2079},[776],[576,2081],{"className":2082,"style":772},[771],[576,2084,2086,2090,2093,2096],{"className":2085},[610],[576,2087],{"className":2088,"style":2089},[614],"height:0.8641em;",[576,2091,1936],{"className":2092},[619],[576,2094],{"className":2095,"style":1826},[771],[576,2097,2099,2105],{"className":2098},[619],[576,2100,2102],{"className":2101},[619,1830],[576,2103,1788],{"className":2104},[619],[576,2106,2108],{"className":2107},[1274],[576,2109,2111],{"className":2110},[801],[576,2112,2114],{"className":2113},[806],[576,2115,2117],{"className":2116,"style":2089},[810],[576,2118,2120,2123],{"style":2119},"top:-3.113em;margin-right:0.05em;",[576,2121],{"className":2122,"style":1291},[818],[576,2124,2126],{"className":2125},[823,824,825,826],[576,2127,742],{"className":2128},[619,826],[563,2130,2131,2132,2207,2208,2251],{},"Ein Drachen hat die Fläche ",[576,2133,2135,2158],{"className":2134},[579],[576,2136,2138],{"className":2137},[583],[585,2139,2140],{"xmlns":587},[589,2141,2142,2155],{},[592,2143,2144,2147,2149],{},[737,2145,2146],{},"24",[1783,2148,1785],{},[1940,2150,2151,2153],{},[1783,2152,1788],{},[737,2154,742],{},[599,2156,2157],{"encoding":601},"24\\,\\text{cm}^2",[576,2159,2161],{"className":2160,"ariaHidden":606},[605],[576,2162,2164,2168,2171,2174],{"className":2163},[610],[576,2165],{"className":2166,"style":2167},[614],"height:0.8141em;",[576,2169,2146],{"className":2170},[619],[576,2172],{"className":2173,"style":1826},[771],[576,2175,2177,2183],{"className":2176},[619],[576,2178,2180],{"className":2179},[619,1830],[576,2181,1788],{"className":2182},[619],[576,2184,2186],{"className":2185},[1274],[576,2187,2189],{"className":2188},[801],[576,2190,2192],{"className":2191},[806],[576,2193,2195],{"className":2194,"style":2167},[810],[576,2196,2198,2201],{"style":2197},"top:-3.063em;margin-right:0.05em;",[576,2199],{"className":2200,"style":1291},[818],[576,2202,2204],{"className":2203},[823,824,825,826],[576,2205,742],{"className":2206},[619,826]," und eine Diagonale von ",[576,2209,2211,2230],{"className":2210},[579],[576,2212,2214],{"className":2213},[583],[585,2215,2216],{"xmlns":587},[589,2217,2218,2227],{},[592,2219,2220,2223,2225],{},[737,2221,2222],{},"8",[1783,2224,1785],{},[1783,2226,1788],{},[599,2228,2229],{"encoding":601},"8\\,\\text{cm}",[576,2231,2233],{"className":2232,"ariaHidden":606},[605],[576,2234,2236,2239,2242,2245],{"className":2235},[610],[576,2237],{"className":2238,"style":1819},[614],[576,2240,2222],{"className":2241},[619],[576,2243],{"className":2244,"style":1826},[771],[576,2246,2248],{"className":2247},[619,1830],[576,2249,1788],{"className":2250},[619],". Die andere Diagonale ist",[576,2253,2255],{"className":2254},[1046],[576,2256,2258,2308],{"className":2257},[579],[576,2259,2261],{"className":2260},[583],[585,2262,2263],{"xmlns":587,"display":1055},[589,2264,2265,2305],{},[592,2266,2267,2269,2271,2283,2285,2297,2299,2301,2303],{},[595,2268,636],{},[730,2270,732],{},[734,2272,2273,2281],{},[592,2274,2275,2277,2279],{},[737,2276,742],{},[730,2278,745],{},[595,2280,728],{},[595,2282,597],{},[730,2284,732],{},[734,2286,2287,2295],{},[592,2288,2289,2291,2293],{},[737,2290,742],{},[730,2292,745],{},[737,2294,2146],{},[737,2296,2222],{},[730,2298,732],{},[737,2300,1781],{},[1783,2302,1785],{},[1783,2304,1788],{},[599,2306,2307],{"encoding":601},"f = \\frac{2 \\cdot A}{e} = \\frac{2 \\cdot 24}{8} = 6\\,\\text{cm}",[576,2309,2311,2329,2420,2509],{"className":2310,"ariaHidden":606},[605],[576,2312,2314,2317,2320,2323,2326],{"className":2313},[610],[576,2315],{"className":2316,"style":648},[614],[576,2318,636],{"className":2319,"style":652},[619,620],[576,2321],{"className":2322,"style":772},[771],[576,2324,732],{"className":2325},[776],[576,2327],{"className":2328,"style":772},[771],[576,2330,2332,2336,2411,2414,2417],{"className":2331},[610],[576,2333],{"className":2334,"style":2335},[614],"height:2.0463em;vertical-align:-0.686em;",[576,2337,2339,2342,2408],{"className":2338},[619],[576,2340],{"className":2341},[793,794],[576,2343,2345],{"className":2344},[734],[576,2346,2348,2400],{"className":2347},[801,802],[576,2349,2351,2397],{"className":2350},[806],[576,2352,2355,2366,2374],{"className":2353,"style":2354},[810],"height:1.3603em;",[576,2356,2357,2360],{"style":1201},[576,2358],{"className":2359,"style":819},[818],[576,2361,2363],{"className":2362},[619],[576,2364,597],{"className":2365},[619,620],[576,2367,2368,2371],{"style":835},[576,2369],{"className":2370,"style":819},[818],[576,2372],{"className":2373,"style":843},[842],[576,2375,2376,2379],{"style":1221},[576,2377],{"className":2378,"style":819},[818],[576,2380,2382,2385,2388,2391,2394],{"className":2381},[619],[576,2383,742],{"className":2384},[619],[576,2386],{"className":2387,"style":880},[771],[576,2389,745],{"className":2390},[884],[576,2392],{"className":2393,"style":880},[771],[576,2395,728],{"className":2396},[619,620],[576,2398,863],{"className":2399},[862],[576,2401,2403],{"className":2402},[806],[576,2404,2406],{"className":2405,"style":1240},[810],[576,2407],{},[576,2409],{"className":2410},[876,794],[576,2412],{"className":2413,"style":772},[771],[576,2415,732],{"className":2416},[776],[576,2418],{"className":2419,"style":772},[771],[576,2421,2423,2426,2500,2503,2506],{"className":2422},[610],[576,2424],{"className":2425,"style":1179},[614],[576,2427,2429,2432,2497],{"className":2428},[619],[576,2430],{"className":2431},[793,794],[576,2433,2435],{"className":2434},[734],[576,2436,2438,2489],{"className":2437},[801,802],[576,2439,2441,2486],{"className":2440},[806],[576,2442,2444,2455,2463],{"className":2443,"style":1198},[810],[576,2445,2446,2449],{"style":1201},[576,2447],{"className":2448,"style":819},[818],[576,2450,2452],{"className":2451},[619],[576,2453,2222],{"className":2454},[619],[576,2456,2457,2460],{"style":835},[576,2458],{"className":2459,"style":819},[818],[576,2461],{"className":2462,"style":843},[842],[576,2464,2465,2468],{"style":1221},[576,2466],{"className":2467,"style":819},[818],[576,2469,2471,2474,2477,2480,2483],{"className":2470},[619],[576,2472,742],{"className":2473},[619],[576,2475],{"className":2476,"style":880},[771],[576,2478,745],{"className":2479},[884],[576,2481],{"className":2482,"style":880},[771],[576,2484,2146],{"className":2485},[619],[576,2487,863],{"className":2488},[862],[576,2490,2492],{"className":2491},[806],[576,2493,2495],{"className":2494,"style":1240},[810],[576,2496],{},[576,2498],{"className":2499},[876,794],[576,2501],{"className":2502,"style":772},[771],[576,2504,732],{"className":2505},[776],[576,2507],{"className":2508,"style":772},[771],[576,2510,2512,2515,2518,2521],{"className":2511},[610],[576,2513],{"className":2514,"style":1819},[614],[576,2516,1781],{"className":2517},[619],[576,2519],{"className":2520,"style":1826},[771],[576,2522,2524],{"className":2523},[619,1830],[576,2525,1788],{"className":2526},[619],[558,2528,2530],{"id":2529},"typische-fehler","Typische Fehler",[2532,2533,2534,2590,2593],"ul",{},[2535,2536,2537,2538,2589],"li",{},"Das Halbieren vergessen: ",[576,2539,2541,2559],{"className":2540},[579],[576,2542,2544],{"className":2543},[583],[585,2545,2546],{"xmlns":587},[589,2547,2548,2556],{},[592,2549,2550,2552,2554],{},[595,2551,597],{},[730,2553,745],{},[595,2555,636],{},[599,2557,2558],{"encoding":601},"e \\cdot f",[576,2560,2562,2580],{"className":2561,"ariaHidden":606},[605],[576,2563,2565,2568,2571,2574,2577],{"className":2564},[610],[576,2566],{"className":2567,"style":894},[614],[576,2569,597],{"className":2570},[619,620],[576,2572],{"className":2573,"style":880},[771],[576,2575,745],{"className":2576},[884],[576,2578],{"className":2579,"style":880},[771],[576,2581,2583,2586],{"className":2582},[610],[576,2584],{"className":2585,"style":648},[614],[576,2587,636],{"className":2588,"style":652},[619,620]," ist die Fläche des umgebenden Rechtecks.",[2535,2591,2592],{},"Seitenlängen statt Diagonalen einsetzen.",[2535,2594,2595,2596,916],{},"Die Einheit: Fläche hat immer eine Quadrat-Einheit, z.B. ",[576,2597,2599,2617],{"className":2598},[579],[576,2600,2602],{"className":2601},[583],[585,2603,2604],{"xmlns":587},[589,2605,2606,2614],{},[592,2607,2608],{},[1940,2609,2610,2612],{},[1783,2611,1788],{},[737,2613,742],{},[599,2615,2616],{"encoding":601},"\\text{cm}^2",[576,2618,2620],{"className":2619,"ariaHidden":606},[605],[576,2621,2623,2626],{"className":2622},[610],[576,2624],{"className":2625,"style":2167},[614],[576,2627,2629,2635],{"className":2628},[619],[576,2630,2632],{"className":2631},[619,1830],[576,2633,1788],{"className":2634},[619],[576,2636,2638],{"className":2637},[1274],[576,2639,2641],{"className":2640},[801],[576,2642,2644],{"className":2643},[806],[576,2645,2647],{"className":2646,"style":2167},[810],[576,2648,2649,2652],{"style":2197},[576,2650],{"className":2651,"style":1291},[818],[576,2653,2655],{"className":2654},[823,824,825,826],[576,2656,742],{"className":2657},[619,826],{"title":2659,"searchDepth":2660,"depth":2660,"links":2661},"",2,[2662,2663,2664,2665],{"id":560,"depth":2660,"text":561},{"id":922,"depth":2660,"text":923},{"id":1758,"depth":2660,"text":1759},{"id":2529,"depth":2660,"text":2530},[2667,2670,2672],{"lhs":2668,"rhs":2669},"1\u002F2*f*x + 1\u002F2*f*y","1\u002F2*(x + y)*f",{"lhs":2671,"rhs":1936},"1\u002F2*6*10",{"lhs":2673,"rhs":1781},"2*24\u002F8",null,"md",{"caption":2677,"x":2678,"y":2681,"items":2684},"Drachenviereck mit den senkrecht aufeinander stehenden Diagonalen e und f",[2679,2680],-2.1,2.1,[2682,2683],-0.5,4.5,[2685,2698,2703,2706,2711,2716],{"type":2686,"points":2687,"fill":2697},"polygon",[2688,2690,2693,2695],[2689,2689],0,[2691,2692],1.5,2.8,[2689,2694],4,[2696,2692],-1.5,true,{"type":2699,"from":2700,"to":2701,"style":2702},"segment",[2689,2689],[2689,2694],"dashed",{"type":2699,"from":2704,"to":2705,"style":2702},[2696,2692],[2691,2692],{"type":2707,"at":2708,"from":2709,"to":2710},"rightAngle",[2689,2692],[2691,2692],[2689,2689],{"type":2712,"at":2713,"text":597},"label",[2714,2715],-0.25,1.3,{"type":2712,"at":2717,"text":636},[2718,2719],-0.75,2.5,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 201.6 240\" width=\"201.6\" height=\"240\" role=\"img\" aria-label=\"Drachenviereck mit den senkrecht aufeinander stehenden Diagonalen e und f\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-kite-area-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-kite-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"201.6\" height=\"240\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"100.8,216 172.8,81.6 100.8,24 28.8,81.6\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"100.8\" y1=\"216\" x2=\"100.8\" y2=\"24\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"28.8\" y1=\"81.6\" x2=\"172.8\" y2=\"81.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 112.8 81.6 L 112.8 93.6 L 100.8 93.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"106.8\" cy=\"87.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"88.8\" y=\"153.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">e\u003C\u002Ftext>\u003Ctext x=\"64.8\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003C\u002Fsvg>","kite-area","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>e\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{1}{2} \\cdot e \\cdot f\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>\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:2.0074em;vertical-align:-0.686em;\">\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:1.3214em;\">\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\">1\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>\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:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">e\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-drachenviereck",[],[2728,2729,2730],"rhombus-area","triangle-area","square-area",{"title":548,"description":2659},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-drachenviereck","Der Flächeninhalt eines Drachenvierecks ist das halbe Produkt seiner beiden Diagonalen.",[2735,2736,2737,2738],"drachenviereck","flächeninhalt","diagonale","viereck",[2740,2743],{"symbol":728,"meaning":2741,"symbolHtml":2742},"Flächeninhalt","\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":2744,"meaning":2745,"symbolHtml":2746},"e, f","Längen der beiden Diagonalen, die senkrecht aufeinander stehen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>e\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e, f\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\">e\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","20PpfJVbIfS-zYO3O6Sq9oUo_dsPQVtfTFp9rieZTiI",[2749,2752,2755],{"stem":2750,"title":2751,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-dreieck","Flächeninhalt eines Dreiecks",{"stem":2753,"title":2754,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-quadrat","Flächeninhalt eines Quadrats",{"stem":2756,"title":2757,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-raute","Flächeninhalt einer Raute",1793824268376]