[{"data":1,"prerenderedAt":4003},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fraumdiagonale-quader":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fraumdiagonale-quader":3990},[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":3844,"conditions":3865,"conditionsHtml":3866,"deprecated":3867,"description":3837,"extension":3868,"figure":3869,"figureCaption":3870,"figureHtml":3960,"formulaId":3961,"latex":3962,"latexHtml":3963,"level":3964,"meta":3965,"navigation":3930,"path":3966,"redirectFrom":3967,"related":3968,"seo":3973,"stem":3974,"subject":589,"summary":3975,"tags":3976,"variables":3981,"__hash__":3989},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fraumdiagonale-quader.md","Raumdiagonale eines Quaders",[550,551,552,553,554],"Raumdiagonale Quader","Raumdiagonale berechnen","d = √(a² + b² + c²)","Quader Diagonale","längste Strecke im Quader",{"type":556,"value":557,"toc":3836},"minimark",[558,563,572,794,798,833,1008,1102,1424,1428,1567,2059,2481,2794,2959,3338,3341,3345],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571],"p",{},"Die ",[568,569,570],"strong",{},"Raumdiagonale"," eines Quaders verläuft durch das Innere des Körpers von einer Ecke zur gegenüberliegenden Ecke. Sie ist die längste Strecke, die in den Quader passt. Ein Quader hat vier Raumdiagonalen, alle gleich lang.",[564,573,574,575,578,579,793],{},"Davon zu unterscheiden sind die ",[568,576,577],{},"Flächendiagonalen",": Sie liegen auf den Seitenflächen, z.B. ",[580,581,584,630],"span",{"className":582},[583],"katex",[580,585,588],{"className":586},[587],"katex-mathml",[589,590,592],"math",{"xmlns":591},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[593,594,595,625],"semantics",{},[596,597,598],"mrow",{},[599,600,601],"msqrt",{},[596,602,603,614,618],{},[604,605,606,610],"msup",{},[607,608,609],"mi",{},"a",[611,612,613],"mn",{},"2",[615,616,617],"mo",{},"+",[604,619,620,623],{},[607,621,622],{},"b",[611,624,613],{},[626,627,629],"annotation",{"encoding":628},"application\u002Fx-tex","\\sqrt{a^2 + b^2}",[580,631,635],{"className":632,"ariaHidden":634},[633],"katex-html","true",[580,636,639,644],{"className":637},[638],"base",[580,640],{"className":641,"style":643},[642],"strut","height:1.04em;vertical-align:-0.1266em;",[580,645,649],{"className":646},[647,648],"mord","sqrt",[580,650,654,784],{"className":651},[652,653],"vlist-t","vlist-t2",[580,655,658,779],{"className":656},[657],"vlist-r",[580,659,663,756],{"className":660,"style":662},[661],"vlist","height:0.9134em;",[580,664,668,673],{"className":665,"style":667},[666],"svg-align","top:-3em;",[580,669],{"className":670,"style":672},[671],"pstrut","height:3em;",[580,674,677,715,720,724,727],{"className":675,"style":676},[647],"padding-left:0.833em;",[580,678,680,684],{"className":679},[647],[580,681,609],{"className":682},[647,683],"mathnormal",[580,685,688],{"className":686},[687],"msupsub",[580,689,691],{"className":690},[652],[580,692,694],{"className":693},[657],[580,695,698],{"className":696,"style":697},[661],"height:0.7401em;",[580,699,701,705],{"style":700},"top:-2.989em;margin-right:0.05em;",[580,702],{"className":703,"style":704},[671],"height:2.7em;",[580,706,712],{"className":707},[708,709,710,711],"sizing","reset-size6","size3","mtight",[580,713,613],{"className":714},[647,711],[580,716],{"className":717,"style":719},[718],"mspace","margin-right:0.2222em;",[580,721,617],{"className":722},[723],"mbin",[580,725],{"className":726,"style":719},[718],[580,728,730,733],{"className":729},[647],[580,731,622],{"className":732},[647,683],[580,734,736],{"className":735},[687],[580,737,739],{"className":738},[652],[580,740,742],{"className":741},[657],[580,743,745],{"className":744,"style":697},[661],[580,746,747,750],{"style":700},[580,748],{"className":749,"style":704},[671],[580,751,753],{"className":752},[708,709,710,711],[580,754,613],{"className":755},[647,711],[580,757,759,762],{"style":758},"top:-2.8734em;",[580,760],{"className":761,"style":672},[671],[580,763,767],{"className":764,"style":766},[765],"hide-tail","min-width:0.853em;height:1.08em;",[768,769,775],"svg",{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[776,777],"path",{"d":778},"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",[580,780,783],{"className":781},[782],"vlist-s","​",[580,785,787],{"className":786},[657],[580,788,791],{"className":789,"style":790},[661],"height:0.1266em;",[580,792],{}," auf der Grundfläche.",[559,795,797],{"id":796},"herleitung","Herleitung",[564,799,800,801,832],{},"Man wendet den Satz des Pythagoras zweimal an. Zuerst auf der Grundfläche für die Flächendiagonale ",[580,802,804,818],{"className":803},[583],[580,805,807],{"className":806},[587],[589,808,809],{"xmlns":591},[593,810,811,816],{},[596,812,813],{},[607,814,815],{},"f",[626,817,815],{"encoding":628},[580,819,821],{"className":820,"ariaHidden":634},[633],[580,822,824,828],{"className":823},[638],[580,825],{"className":826,"style":827},[642],"height:0.8889em;vertical-align:-0.1944em;",[580,829,815],{"className":830,"style":831},[647,683],"margin-right:0.1076em;",":",[580,834,837],{"className":835},[836],"katex-display",[580,838,840,876],{"className":839},[583],[580,841,843],{"className":842},[587],[589,844,846],{"xmlns":591,"display":845},"block",[593,847,848,873],{},[596,849,850,856,859,865,867],{},[604,851,852,854],{},[607,853,815],{},[611,855,613],{},[615,857,858],{},"=",[604,860,861,863],{},[607,862,609],{},[611,864,613],{},[615,866,617],{},[604,868,869,871],{},[607,870,622],{},[611,872,613],{},[626,874,875],{"encoding":628},"f^2 = a^2 + b^2",[580,877,879,928,973],{"className":878,"ariaHidden":634},[633],[580,880,882,886,917,921,925],{"className":881},[638],[580,883],{"className":884,"style":885},[642],"height:1.0585em;vertical-align:-0.1944em;",[580,887,889,892],{"className":888},[647],[580,890,815],{"className":891,"style":831},[647,683],[580,893,895],{"className":894},[687],[580,896,898],{"className":897},[652],[580,899,901],{"className":900},[657],[580,902,905],{"className":903,"style":904},[661],"height:0.8641em;",[580,906,908,911],{"style":907},"top:-3.113em;margin-right:0.05em;",[580,909],{"className":910,"style":704},[671],[580,912,914],{"className":913},[708,709,710,711],[580,915,613],{"className":916},[647,711],[580,918],{"className":919,"style":920},[718],"margin-right:0.2778em;",[580,922,858],{"className":923},[924],"mrel",[580,926],{"className":927,"style":920},[718],[580,929,931,935,964,967,970],{"className":930},[638],[580,932],{"className":933,"style":934},[642],"height:0.9474em;vertical-align:-0.0833em;",[580,936,938,941],{"className":937},[647],[580,939,609],{"className":940},[647,683],[580,942,944],{"className":943},[687],[580,945,947],{"className":946},[652],[580,948,950],{"className":949},[657],[580,951,953],{"className":952,"style":904},[661],[580,954,955,958],{"style":907},[580,956],{"className":957,"style":704},[671],[580,959,961],{"className":960},[708,709,710,711],[580,962,613],{"className":963},[647,711],[580,965],{"className":966,"style":719},[718],[580,968,617],{"className":969},[723],[580,971],{"className":972,"style":719},[718],[580,974,976,979],{"className":975},[638],[580,977],{"className":978,"style":904},[642],[580,980,982,985],{"className":981},[647],[580,983,622],{"className":984},[647,683],[580,986,988],{"className":987},[687],[580,989,991],{"className":990},[652],[580,992,994],{"className":993},[657],[580,995,997],{"className":996,"style":904},[661],[580,998,999,1002],{"style":907},[580,1000],{"className":1001,"style":704},[671],[580,1003,1005],{"className":1004},[708,709,710,711],[580,1006,613],{"className":1007},[647,711],[564,1009,1010,1011,1039,1040,1070,1071,1101],{},"Die Flächendiagonale ",[580,1012,1014,1027],{"className":1013},[583],[580,1015,1017],{"className":1016},[587],[589,1018,1019],{"xmlns":591},[593,1020,1021,1025],{},[596,1022,1023],{},[607,1024,815],{},[626,1026,815],{"encoding":628},[580,1028,1030],{"className":1029,"ariaHidden":634},[633],[580,1031,1033,1036],{"className":1032},[638],[580,1034],{"className":1035,"style":827},[642],[580,1037,815],{"className":1038,"style":831},[647,683],", die Höhe ",[580,1041,1043,1057],{"className":1042},[583],[580,1044,1046],{"className":1045},[587],[589,1047,1048],{"xmlns":591},[593,1049,1050,1055],{},[596,1051,1052],{},[607,1053,1054],{},"c",[626,1056,1054],{"encoding":628},[580,1058,1060],{"className":1059,"ariaHidden":634},[633],[580,1061,1063,1067],{"className":1062},[638],[580,1064],{"className":1065,"style":1066},[642],"height:0.4306em;",[580,1068,1054],{"className":1069},[647,683]," und die Raumdiagonale ",[580,1072,1074,1088],{"className":1073},[583],[580,1075,1077],{"className":1076},[587],[589,1078,1079],{"xmlns":591},[593,1080,1081,1086],{},[596,1082,1083],{},[607,1084,1085],{},"d",[626,1087,1085],{"encoding":628},[580,1089,1091],{"className":1090,"ariaHidden":634},[633],[580,1092,1094,1098],{"className":1093},[638],[580,1095],{"className":1096,"style":1097},[642],"height:0.6944em;",[580,1099,1085],{"className":1100},[647,683]," bilden ein rechtwinkliges Dreieck, das senkrecht im Quader steht:",[580,1103,1105],{"className":1104},[836],[580,1106,1108,1166],{"className":1107},[583],[580,1109,1111],{"className":1110},[587],[589,1112,1113],{"xmlns":591,"display":845},[593,1114,1115,1163],{},[596,1116,1117,1123,1125,1131,1133,1139,1141,1147,1149,1155,1157],{},[604,1118,1119,1121],{},[607,1120,1085],{},[611,1122,613],{},[615,1124,858],{},[604,1126,1127,1129],{},[607,1128,815],{},[611,1130,613],{},[615,1132,617],{},[604,1134,1135,1137],{},[607,1136,1054],{},[611,1138,613],{},[615,1140,858],{},[604,1142,1143,1145],{},[607,1144,609],{},[611,1146,613],{},[615,1148,617],{},[604,1150,1151,1153],{},[607,1152,622],{},[611,1154,613],{},[615,1156,617],{},[604,1158,1159,1161],{},[607,1160,1054],{},[611,1162,613],{},[626,1164,1165],{"encoding":628},"d^2 = f^2 + c^2 = a^2 + b^2 + c^2",[580,1167,1169,1213,1257,1301,1345,1389],{"className":1168,"ariaHidden":634},[633],[580,1170,1172,1175,1204,1207,1210],{"className":1171},[638],[580,1173],{"className":1174,"style":904},[642],[580,1176,1178,1181],{"className":1177},[647],[580,1179,1085],{"className":1180},[647,683],[580,1182,1184],{"className":1183},[687],[580,1185,1187],{"className":1186},[652],[580,1188,1190],{"className":1189},[657],[580,1191,1193],{"className":1192,"style":904},[661],[580,1194,1195,1198],{"style":907},[580,1196],{"className":1197,"style":704},[671],[580,1199,1201],{"className":1200},[708,709,710,711],[580,1202,613],{"className":1203},[647,711],[580,1205],{"className":1206,"style":920},[718],[580,1208,858],{"className":1209},[924],[580,1211],{"className":1212,"style":920},[718],[580,1214,1216,1219,1248,1251,1254],{"className":1215},[638],[580,1217],{"className":1218,"style":885},[642],[580,1220,1222,1225],{"className":1221},[647],[580,1223,815],{"className":1224,"style":831},[647,683],[580,1226,1228],{"className":1227},[687],[580,1229,1231],{"className":1230},[652],[580,1232,1234],{"className":1233},[657],[580,1235,1237],{"className":1236,"style":904},[661],[580,1238,1239,1242],{"style":907},[580,1240],{"className":1241,"style":704},[671],[580,1243,1245],{"className":1244},[708,709,710,711],[580,1246,613],{"className":1247},[647,711],[580,1249],{"className":1250,"style":719},[718],[580,1252,617],{"className":1253},[723],[580,1255],{"className":1256,"style":719},[718],[580,1258,1260,1263,1292,1295,1298],{"className":1259},[638],[580,1261],{"className":1262,"style":904},[642],[580,1264,1266,1269],{"className":1265},[647],[580,1267,1054],{"className":1268},[647,683],[580,1270,1272],{"className":1271},[687],[580,1273,1275],{"className":1274},[652],[580,1276,1278],{"className":1277},[657],[580,1279,1281],{"className":1280,"style":904},[661],[580,1282,1283,1286],{"style":907},[580,1284],{"className":1285,"style":704},[671],[580,1287,1289],{"className":1288},[708,709,710,711],[580,1290,613],{"className":1291},[647,711],[580,1293],{"className":1294,"style":920},[718],[580,1296,858],{"className":1297},[924],[580,1299],{"className":1300,"style":920},[718],[580,1302,1304,1307,1336,1339,1342],{"className":1303},[638],[580,1305],{"className":1306,"style":934},[642],[580,1308,1310,1313],{"className":1309},[647],[580,1311,609],{"className":1312},[647,683],[580,1314,1316],{"className":1315},[687],[580,1317,1319],{"className":1318},[652],[580,1320,1322],{"className":1321},[657],[580,1323,1325],{"className":1324,"style":904},[661],[580,1326,1327,1330],{"style":907},[580,1328],{"className":1329,"style":704},[671],[580,1331,1333],{"className":1332},[708,709,710,711],[580,1334,613],{"className":1335},[647,711],[580,1337],{"className":1338,"style":719},[718],[580,1340,617],{"className":1341},[723],[580,1343],{"className":1344,"style":719},[718],[580,1346,1348,1351,1380,1383,1386],{"className":1347},[638],[580,1349],{"className":1350,"style":934},[642],[580,1352,1354,1357],{"className":1353},[647],[580,1355,622],{"className":1356},[647,683],[580,1358,1360],{"className":1359},[687],[580,1361,1363],{"className":1362},[652],[580,1364,1366],{"className":1365},[657],[580,1367,1369],{"className":1368,"style":904},[661],[580,1370,1371,1374],{"style":907},[580,1372],{"className":1373,"style":704},[671],[580,1375,1377],{"className":1376},[708,709,710,711],[580,1378,613],{"className":1379},[647,711],[580,1381],{"className":1382,"style":719},[718],[580,1384,617],{"className":1385},[723],[580,1387],{"className":1388,"style":719},[718],[580,1390,1392,1395],{"className":1391},[638],[580,1393],{"className":1394,"style":904},[642],[580,1396,1398,1401],{"className":1397},[647],[580,1399,1054],{"className":1400},[647,683],[580,1402,1404],{"className":1403},[687],[580,1405,1407],{"className":1406},[652],[580,1408,1410],{"className":1409},[657],[580,1411,1413],{"className":1412,"style":904},[661],[580,1414,1415,1418],{"style":907},[580,1416],{"className":1417,"style":704},[671],[580,1419,1421],{"className":1420},[708,709,710,711],[580,1422,613],{"className":1423},[647,711],[559,1425,1427],{"id":1426},"beispiele","Beispiele",[564,1429,1430,1431,1479,1480,1523,1524,832],{},"Ein Quader hat die Kanten ",[580,1432,1434,1455],{"className":1433},[583],[580,1435,1437],{"className":1436},[587],[589,1438,1439],{"xmlns":591},[593,1440,1441,1452],{},[596,1442,1443,1445,1449],{},[611,1444,613],{},[1446,1447,1448],"mtext",{}," ",[1446,1450,1451],{},"cm",[626,1453,1454],{"encoding":628},"2\\,\\text{cm}",[580,1456,1458],{"className":1457,"ariaHidden":634},[633],[580,1459,1461,1465,1468,1472],{"className":1460},[638],[580,1462],{"className":1463,"style":1464},[642],"height:0.6444em;",[580,1466,613],{"className":1467},[647],[580,1469],{"className":1470,"style":1471},[718],"margin-right:0.1667em;",[580,1473,1476],{"className":1474},[647,1475],"text",[580,1477,1451],{"className":1478},[647],", ",[580,1481,1483,1502],{"className":1482},[583],[580,1484,1486],{"className":1485},[587],[589,1487,1488],{"xmlns":591},[593,1489,1490,1499],{},[596,1491,1492,1495,1497],{},[611,1493,1494],{},"3",[1446,1496,1448],{},[1446,1498,1451],{},[626,1500,1501],{"encoding":628},"3\\,\\text{cm}",[580,1503,1505],{"className":1504,"ariaHidden":634},[633],[580,1506,1508,1511,1514,1517],{"className":1507},[638],[580,1509],{"className":1510,"style":1464},[642],[580,1512,1494],{"className":1513},[647],[580,1515],{"className":1516,"style":1471},[718],[580,1518,1520],{"className":1519},[647,1475],[580,1521,1451],{"className":1522},[647]," und ",[580,1525,1527,1546],{"className":1526},[583],[580,1528,1530],{"className":1529},[587],[589,1531,1532],{"xmlns":591},[593,1533,1534,1543],{},[596,1535,1536,1539,1541],{},[611,1537,1538],{},"6",[1446,1540,1448],{},[1446,1542,1451],{},[626,1544,1545],{"encoding":628},"6\\,\\text{cm}",[580,1547,1549],{"className":1548,"ariaHidden":634},[633],[580,1550,1552,1555,1558,1561],{"className":1551},[638],[580,1553],{"className":1554,"style":1464},[642],[580,1556,1538],{"className":1557},[647],[580,1559],{"className":1560,"style":1471},[718],[580,1562,1564],{"className":1563},[647,1475],[580,1565,1451],{"className":1566},[647],[580,1568,1570],{"className":1569},[836],[580,1571,1573,1662],{"className":1572},[583],[580,1574,1576],{"className":1575},[587],[589,1577,1578],{"xmlns":591,"display":845},[593,1579,1580,1659],{},[596,1581,1582,1584,1586,1612,1614,1616,1618,1635,1637,1639,1641,1646,1648,1650,1652,1655,1657],{},[607,1583,1085],{},[615,1585,858],{},[599,1587,1588],{},[596,1589,1590,1596,1598,1604,1606],{},[604,1591,1592,1594],{},[611,1593,613],{},[611,1595,613],{},[615,1597,617],{},[604,1599,1600,1602],{},[611,1601,1494],{},[611,1603,613],{},[615,1605,617],{},[604,1607,1608,1610],{},[611,1609,1538],{},[611,1611,613],{},[1446,1613,1448],{},[1446,1615,1451],{},[615,1617,858],{},[599,1619,1620],{},[596,1621,1622,1625,1627,1630,1632],{},[611,1623,1624],{},"4",[615,1626,617],{},[611,1628,1629],{},"9",[615,1631,617],{},[611,1633,1634],{},"36",[1446,1636,1448],{},[1446,1638,1451],{},[615,1640,858],{},[599,1642,1643],{},[611,1644,1645],{},"49",[1446,1647,1448],{},[1446,1649,1451],{},[615,1651,858],{},[611,1653,1654],{},"7",[1446,1656,1448],{},[1446,1658,1451],{},[626,1660,1661],{"encoding":628},"d = \\sqrt{2^2 + 3^2 + 6^2}\\,\\text{cm} = \\sqrt{4 + 9 + 36}\\,\\text{cm} = \\sqrt{49}\\,\\text{cm} = 7\\,\\text{cm}",[580,1663,1665,1683,1867,1966,2041],{"className":1664,"ariaHidden":634},[633],[580,1666,1668,1671,1674,1677,1680],{"className":1667},[638],[580,1669],{"className":1670,"style":1097},[642],[580,1672,1085],{"className":1673},[647,683],[580,1675],{"className":1676,"style":920},[718],[580,1678,858],{"className":1679},[924],[580,1681],{"className":1682,"style":920},[718],[580,1684,1686,1690,1849,1852,1858,1861,1864],{"className":1685},[638],[580,1687],{"className":1688,"style":1689},[642],"height:1.24em;vertical-align:-0.1777em;",[580,1691,1693],{"className":1692},[647,648],[580,1694,1696,1840],{"className":1695},[652,653],[580,1697,1699,1837],{"className":1698},[657],[580,1700,1703,1820],{"className":1701,"style":1702},[661],"height:1.0623em;",[580,1704,1707,1711],{"className":1705,"style":1706},[666],"top:-3.2em;",[580,1708],{"className":1709,"style":1710},[671],"height:3.2em;",[580,1712,1715,1744,1747,1750,1753,1782,1785,1788,1791],{"className":1713,"style":1714},[647],"padding-left:1em;",[580,1716,1718,1721],{"className":1717},[647],[580,1719,613],{"className":1720},[647],[580,1722,1724],{"className":1723},[687],[580,1725,1727],{"className":1726},[652],[580,1728,1730],{"className":1729},[657],[580,1731,1733],{"className":1732,"style":697},[661],[580,1734,1735,1738],{"style":700},[580,1736],{"className":1737,"style":704},[671],[580,1739,1741],{"className":1740},[708,709,710,711],[580,1742,613],{"className":1743},[647,711],[580,1745],{"className":1746,"style":719},[718],[580,1748,617],{"className":1749},[723],[580,1751],{"className":1752,"style":719},[718],[580,1754,1756,1759],{"className":1755},[647],[580,1757,1494],{"className":1758},[647],[580,1760,1762],{"className":1761},[687],[580,1763,1765],{"className":1764},[652],[580,1766,1768],{"className":1767},[657],[580,1769,1771],{"className":1770,"style":697},[661],[580,1772,1773,1776],{"style":700},[580,1774],{"className":1775,"style":704},[671],[580,1777,1779],{"className":1778},[708,709,710,711],[580,1780,613],{"className":1781},[647,711],[580,1783],{"className":1784,"style":719},[718],[580,1786,617],{"className":1787},[723],[580,1789],{"className":1790,"style":719},[718],[580,1792,1794,1797],{"className":1793},[647],[580,1795,1538],{"className":1796},[647],[580,1798,1800],{"className":1799},[687],[580,1801,1803],{"className":1802},[652],[580,1804,1806],{"className":1805},[657],[580,1807,1809],{"className":1808,"style":697},[661],[580,1810,1811,1814],{"style":700},[580,1812],{"className":1813,"style":704},[671],[580,1815,1817],{"className":1816},[708,709,710,711],[580,1818,613],{"className":1819},[647,711],[580,1821,1823,1826],{"style":1822},"top:-3.0223em;",[580,1824],{"className":1825,"style":1710},[671],[580,1827,1830],{"className":1828,"style":1829},[765],"min-width:1.02em;height:1.28em;",[768,1831,1834],{"xmlns":770,"width":771,"height":1832,"viewBox":1833,"preserveAspectRatio":774},"1.28em","0 0 400000 1296",[776,1835],{"d":1836},"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",[580,1838,783],{"className":1839},[782],[580,1841,1843],{"className":1842},[657],[580,1844,1847],{"className":1845,"style":1846},[661],"height:0.1777em;",[580,1848],{},[580,1850],{"className":1851,"style":1471},[718],[580,1853,1855],{"className":1854},[647,1475],[580,1856,1451],{"className":1857},[647],[580,1859],{"className":1860,"style":920},[718],[580,1862,858],{"className":1863},[924],[580,1865],{"className":1866,"style":920},[718],[580,1868,1870,1874,1948,1951,1957,1960,1963],{"className":1869},[638],[580,1871],{"className":1872,"style":1873},[642],"height:1.04em;vertical-align:-0.1256em;",[580,1875,1877],{"className":1876},[647,648],[580,1878,1880,1939],{"className":1879},[652,653],[580,1881,1883,1936],{"className":1882},[657],[580,1884,1887,1923],{"className":1885,"style":1886},[661],"height:0.9144em;",[580,1888,1890,1893],{"className":1889,"style":667},[666],[580,1891],{"className":1892,"style":672},[671],[580,1894,1896,1899,1902,1905,1908,1911,1914,1917,1920],{"className":1895,"style":676},[647],[580,1897,1624],{"className":1898},[647],[580,1900],{"className":1901,"style":719},[718],[580,1903,617],{"className":1904},[723],[580,1906],{"className":1907,"style":719},[718],[580,1909,1629],{"className":1910},[647],[580,1912],{"className":1913,"style":719},[718],[580,1915,617],{"className":1916},[723],[580,1918],{"className":1919,"style":719},[718],[580,1921,1634],{"className":1922},[647],[580,1924,1926,1929],{"style":1925},"top:-2.8744em;",[580,1927],{"className":1928,"style":672},[671],[580,1930,1932],{"className":1931,"style":766},[765],[768,1933,1934],{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},[776,1935],{"d":778},[580,1937,783],{"className":1938},[782],[580,1940,1942],{"className":1941},[657],[580,1943,1946],{"className":1944,"style":1945},[661],"height:0.1256em;",[580,1947],{},[580,1949],{"className":1950,"style":1471},[718],[580,1952,1954],{"className":1953},[647,1475],[580,1955,1451],{"className":1956},[647],[580,1958],{"className":1959,"style":920},[718],[580,1961,858],{"className":1962},[924],[580,1964],{"className":1965,"style":920},[718],[580,1967,1969,1973,2023,2026,2032,2035,2038],{"className":1968},[638],[580,1970],{"className":1971,"style":1972},[642],"height:1.04em;vertical-align:-0.0839em;",[580,1974,1976],{"className":1975},[647,648],[580,1977,1979,2014],{"className":1978},[652,653],[580,1980,1982,2011],{"className":1981},[657],[580,1983,1986,1998],{"className":1984,"style":1985},[661],"height:0.9561em;",[580,1987,1989,1992],{"className":1988,"style":667},[666],[580,1990],{"className":1991,"style":672},[671],[580,1993,1995],{"className":1994,"style":676},[647],[580,1996,1645],{"className":1997},[647],[580,1999,2001,2004],{"style":2000},"top:-2.9161em;",[580,2002],{"className":2003,"style":672},[671],[580,2005,2007],{"className":2006,"style":766},[765],[768,2008,2009],{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},[776,2010],{"d":778},[580,2012,783],{"className":2013},[782],[580,2015,2017],{"className":2016},[657],[580,2018,2021],{"className":2019,"style":2020},[661],"height:0.0839em;",[580,2022],{},[580,2024],{"className":2025,"style":1471},[718],[580,2027,2029],{"className":2028},[647,1475],[580,2030,1451],{"className":2031},[647],[580,2033],{"className":2034,"style":920},[718],[580,2036,858],{"className":2037},[924],[580,2039],{"className":2040,"style":920},[718],[580,2042,2044,2047,2050,2053],{"className":2043},[638],[580,2045],{"className":2046,"style":1464},[642],[580,2048,1654],{"className":2049},[647],[580,2051],{"className":2052,"style":1471},[718],[580,2054,2056],{"className":2055},[647,1475],[580,2057,1451],{"className":2058},[647],[564,2060,2061,2062,1479,2126,1523,2190,2255,2256,2480],{},"Für einen Quader mit ",[580,2063,2065,2087],{"className":2064},[583],[580,2066,2068],{"className":2067},[587],[589,2069,2070],{"xmlns":591},[593,2071,2072,2084],{},[596,2073,2074,2076,2078,2080,2082],{},[607,2075,609],{},[615,2077,858],{},[611,2079,1624],{},[1446,2081,1448],{},[1446,2083,1451],{},[626,2085,2086],{"encoding":628},"a = 4\\,\\text{cm}",[580,2088,2090,2108],{"className":2089,"ariaHidden":634},[633],[580,2091,2093,2096,2099,2102,2105],{"className":2092},[638],[580,2094],{"className":2095,"style":1066},[642],[580,2097,609],{"className":2098},[647,683],[580,2100],{"className":2101,"style":920},[718],[580,2103,858],{"className":2104},[924],[580,2106],{"className":2107,"style":920},[718],[580,2109,2111,2114,2117,2120],{"className":2110},[638],[580,2112],{"className":2113,"style":1464},[642],[580,2115,1624],{"className":2116},[647],[580,2118],{"className":2119,"style":1471},[718],[580,2121,2123],{"className":2122},[647,1475],[580,2124,1451],{"className":2125},[647],[580,2127,2129,2151],{"className":2128},[583],[580,2130,2132],{"className":2131},[587],[589,2133,2134],{"xmlns":591},[593,2135,2136,2148],{},[596,2137,2138,2140,2142,2144,2146],{},[607,2139,622],{},[615,2141,858],{},[611,2143,1494],{},[1446,2145,1448],{},[1446,2147,1451],{},[626,2149,2150],{"encoding":628},"b = 3\\,\\text{cm}",[580,2152,2154,2172],{"className":2153,"ariaHidden":634},[633],[580,2155,2157,2160,2163,2166,2169],{"className":2156},[638],[580,2158],{"className":2159,"style":1097},[642],[580,2161,622],{"className":2162},[647,683],[580,2164],{"className":2165,"style":920},[718],[580,2167,858],{"className":2168},[924],[580,2170],{"className":2171,"style":920},[718],[580,2173,2175,2178,2181,2184],{"className":2174},[638],[580,2176],{"className":2177,"style":1464},[642],[580,2179,1494],{"className":2180},[647],[580,2182],{"className":2183,"style":1471},[718],[580,2185,2187],{"className":2186},[647,1475],[580,2188,1451],{"className":2189},[647],[580,2191,2193,2216],{"className":2192},[583],[580,2194,2196],{"className":2195},[587],[589,2197,2198],{"xmlns":591},[593,2199,2200,2213],{},[596,2201,2202,2204,2206,2209,2211],{},[607,2203,1054],{},[615,2205,858],{},[611,2207,2208],{},"12",[1446,2210,1448],{},[1446,2212,1451],{},[626,2214,2215],{"encoding":628},"c = 12\\,\\text{cm}",[580,2217,2219,2237],{"className":2218,"ariaHidden":634},[633],[580,2220,2222,2225,2228,2231,2234],{"className":2221},[638],[580,2223],{"className":2224,"style":1066},[642],[580,2226,1054],{"className":2227},[647,683],[580,2229],{"className":2230,"style":920},[718],[580,2232,858],{"className":2233},[924],[580,2235],{"className":2236,"style":920},[718],[580,2238,2240,2243,2246,2249],{"className":2239},[638],[580,2241],{"className":2242,"style":1464},[642],[580,2244,2208],{"className":2245},[647],[580,2247],{"className":2248,"style":1471},[718],[580,2250,2252],{"className":2251},[647,1475],[580,2253,1451],{"className":2254},[647]," in zwei Schritten: Die Flächendiagonale ist ",[580,2257,2259,2306],{"className":2258},[583],[580,2260,2262],{"className":2261},[587],[589,2263,2264],{"xmlns":591},[593,2265,2266,2303],{},[596,2267,2268,2270,2272,2290,2292,2294,2296,2299,2301],{},[607,2269,815],{},[615,2271,858],{},[599,2273,2274],{},[596,2275,2276,2282,2284],{},[604,2277,2278,2280],{},[611,2279,1624],{},[611,2281,613],{},[615,2283,617],{},[604,2285,2286,2288],{},[611,2287,1494],{},[611,2289,613],{},[1446,2291,1448],{},[1446,2293,1451],{},[615,2295,858],{},[611,2297,2298],{},"5",[1446,2300,1448],{},[1446,2302,1451],{},[626,2304,2305],{"encoding":628},"f = \\sqrt{4^2 + 3^2}\\,\\text{cm} = 5\\,\\text{cm}",[580,2307,2309,2327,2462],{"className":2308,"ariaHidden":634},[633],[580,2310,2312,2315,2318,2321,2324],{"className":2311},[638],[580,2313],{"className":2314,"style":827},[642],[580,2316,815],{"className":2317,"style":831},[647,683],[580,2319],{"className":2320,"style":920},[718],[580,2322,858],{"className":2323},[924],[580,2325],{"className":2326,"style":920},[718],[580,2328,2330,2333,2444,2447,2453,2456,2459],{"className":2329},[638],[580,2331],{"className":2332,"style":643},[642],[580,2334,2336],{"className":2335},[647,648],[580,2337,2339,2436],{"className":2338},[652,653],[580,2340,2342,2433],{"className":2341},[657],[580,2343,2345,2421],{"className":2344,"style":662},[661],[580,2346,2348,2351],{"className":2347,"style":667},[666],[580,2349],{"className":2350,"style":672},[671],[580,2352,2354,2383,2386,2389,2392],{"className":2353,"style":676},[647],[580,2355,2357,2360],{"className":2356},[647],[580,2358,1624],{"className":2359},[647],[580,2361,2363],{"className":2362},[687],[580,2364,2366],{"className":2365},[652],[580,2367,2369],{"className":2368},[657],[580,2370,2372],{"className":2371,"style":697},[661],[580,2373,2374,2377],{"style":700},[580,2375],{"className":2376,"style":704},[671],[580,2378,2380],{"className":2379},[708,709,710,711],[580,2381,613],{"className":2382},[647,711],[580,2384],{"className":2385,"style":719},[718],[580,2387,617],{"className":2388},[723],[580,2390],{"className":2391,"style":719},[718],[580,2393,2395,2398],{"className":2394},[647],[580,2396,1494],{"className":2397},[647],[580,2399,2401],{"className":2400},[687],[580,2402,2404],{"className":2403},[652],[580,2405,2407],{"className":2406},[657],[580,2408,2410],{"className":2409,"style":697},[661],[580,2411,2412,2415],{"style":700},[580,2413],{"className":2414,"style":704},[671],[580,2416,2418],{"className":2417},[708,709,710,711],[580,2419,613],{"className":2420},[647,711],[580,2422,2423,2426],{"style":758},[580,2424],{"className":2425,"style":672},[671],[580,2427,2429],{"className":2428,"style":766},[765],[768,2430,2431],{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},[776,2432],{"d":778},[580,2434,783],{"className":2435},[782],[580,2437,2439],{"className":2438},[657],[580,2440,2442],{"className":2441,"style":790},[661],[580,2443],{},[580,2445],{"className":2446,"style":1471},[718],[580,2448,2450],{"className":2449},[647,1475],[580,2451,1451],{"className":2452},[647],[580,2454],{"className":2455,"style":920},[718],[580,2457,858],{"className":2458},[924],[580,2460],{"className":2461,"style":920},[718],[580,2463,2465,2468,2471,2474],{"className":2464},[638],[580,2466],{"className":2467,"style":1464},[642],[580,2469,2298],{"className":2470},[647],[580,2472],{"className":2473,"style":1471},[718],[580,2475,2477],{"className":2476},[647,1475],[580,2478,1451],{"className":2479},[647],", die Raumdiagonale",[580,2482,2484],{"className":2483},[836],[580,2485,2487,2545],{"className":2486},[583],[580,2488,2490],{"className":2489},[587],[589,2491,2492],{"xmlns":591,"display":845},[593,2493,2494,2542],{},[596,2495,2496,2498,2500,2518,2520,2522,2524,2529,2531,2533,2535,2538,2540],{},[607,2497,1085],{},[615,2499,858],{},[599,2501,2502],{},[596,2503,2504,2510,2512],{},[604,2505,2506,2508],{},[611,2507,2298],{},[611,2509,613],{},[615,2511,617],{},[604,2513,2514,2516],{},[611,2515,2208],{},[611,2517,613],{},[1446,2519,1448],{},[1446,2521,1451],{},[615,2523,858],{},[599,2525,2526],{},[611,2527,2528],{},"169",[1446,2530,1448],{},[1446,2532,1451],{},[615,2534,858],{},[611,2536,2537],{},"13",[1446,2539,1448],{},[1446,2541,1451],{},[626,2543,2544],{"encoding":628},"d = \\sqrt{5^2 + 12^2}\\,\\text{cm} = \\sqrt{169}\\,\\text{cm} = 13\\,\\text{cm}",[580,2546,2548,2566,2705,2776],{"className":2547,"ariaHidden":634},[633],[580,2549,2551,2554,2557,2560,2563],{"className":2550},[638],[580,2552],{"className":2553,"style":1097},[642],[580,2555,1085],{"className":2556},[647,683],[580,2558],{"className":2559,"style":920},[718],[580,2561,858],{"className":2562},[924],[580,2564],{"className":2565,"style":920},[718],[580,2567,2569,2572,2687,2690,2696,2699,2702],{"className":2568},[638],[580,2570],{"className":2571,"style":1689},[642],[580,2573,2575],{"className":2574},[647,648],[580,2576,2578,2679],{"className":2577},[652,653],[580,2579,2581,2676],{"className":2580},[657],[580,2582,2584,2664],{"className":2583,"style":1702},[661],[580,2585,2587,2590],{"className":2586,"style":1706},[666],[580,2588],{"className":2589,"style":1710},[671],[580,2591,2593,2622,2625,2628,2631,2635],{"className":2592,"style":1714},[647],[580,2594,2596,2599],{"className":2595},[647],[580,2597,2298],{"className":2598},[647],[580,2600,2602],{"className":2601},[687],[580,2603,2605],{"className":2604},[652],[580,2606,2608],{"className":2607},[657],[580,2609,2611],{"className":2610,"style":697},[661],[580,2612,2613,2616],{"style":700},[580,2614],{"className":2615,"style":704},[671],[580,2617,2619],{"className":2618},[708,709,710,711],[580,2620,613],{"className":2621},[647,711],[580,2623],{"className":2624,"style":719},[718],[580,2626,617],{"className":2627},[723],[580,2629],{"className":2630,"style":719},[718],[580,2632,2634],{"className":2633},[647],"1",[580,2636,2638,2641],{"className":2637},[647],[580,2639,613],{"className":2640},[647],[580,2642,2644],{"className":2643},[687],[580,2645,2647],{"className":2646},[652],[580,2648,2650],{"className":2649},[657],[580,2651,2653],{"className":2652,"style":697},[661],[580,2654,2655,2658],{"style":700},[580,2656],{"className":2657,"style":704},[671],[580,2659,2661],{"className":2660},[708,709,710,711],[580,2662,613],{"className":2663},[647,711],[580,2665,2666,2669],{"style":1822},[580,2667],{"className":2668,"style":1710},[671],[580,2670,2672],{"className":2671,"style":1829},[765],[768,2673,2674],{"xmlns":770,"width":771,"height":1832,"viewBox":1833,"preserveAspectRatio":774},[776,2675],{"d":1836},[580,2677,783],{"className":2678},[782],[580,2680,2682],{"className":2681},[657],[580,2683,2685],{"className":2684,"style":1846},[661],[580,2686],{},[580,2688],{"className":2689,"style":1471},[718],[580,2691,2693],{"className":2692},[647,1475],[580,2694,1451],{"className":2695},[647],[580,2697],{"className":2698,"style":920},[718],[580,2700,858],{"className":2701},[924],[580,2703],{"className":2704,"style":920},[718],[580,2706,2708,2711,2758,2761,2767,2770,2773],{"className":2707},[638],[580,2709],{"className":2710,"style":1972},[642],[580,2712,2714],{"className":2713},[647,648],[580,2715,2717,2750],{"className":2716},[652,653],[580,2718,2720,2747],{"className":2719},[657],[580,2721,2723,2735],{"className":2722,"style":1985},[661],[580,2724,2726,2729],{"className":2725,"style":667},[666],[580,2727],{"className":2728,"style":672},[671],[580,2730,2732],{"className":2731,"style":676},[647],[580,2733,2528],{"className":2734},[647],[580,2736,2737,2740],{"style":2000},[580,2738],{"className":2739,"style":672},[671],[580,2741,2743],{"className":2742,"style":766},[765],[768,2744,2745],{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},[776,2746],{"d":778},[580,2748,783],{"className":2749},[782],[580,2751,2753],{"className":2752},[657],[580,2754,2756],{"className":2755,"style":2020},[661],[580,2757],{},[580,2759],{"className":2760,"style":1471},[718],[580,2762,2764],{"className":2763},[647,1475],[580,2765,1451],{"className":2766},[647],[580,2768],{"className":2769,"style":920},[718],[580,2771,858],{"className":2772},[924],[580,2774],{"className":2775,"style":920},[718],[580,2777,2779,2782,2785,2788],{"className":2778},[638],[580,2780],{"className":2781,"style":1464},[642],[580,2783,2537],{"className":2784},[647],[580,2786],{"className":2787,"style":1471},[718],[580,2789,2791],{"className":2790},[647,1475],[580,2792,1451],{"className":2793},[647],[564,2795,2796,2797,2840,2841,2958],{},"Passt ein ",[580,2798,2800,2819],{"className":2799},[583],[580,2801,2803],{"className":2802},[587],[589,2804,2805],{"xmlns":591},[593,2806,2807,2816],{},[596,2808,2809,2812,2814],{},[611,2810,2811],{},"75",[1446,2813,1448],{},[1446,2815,1451],{},[626,2817,2818],{"encoding":628},"75\\,\\text{cm}",[580,2820,2822],{"className":2821,"ariaHidden":634},[633],[580,2823,2825,2828,2831,2834],{"className":2824},[638],[580,2826],{"className":2827,"style":1464},[642],[580,2829,2811],{"className":2830},[647],[580,2832],{"className":2833,"style":1471},[718],[580,2835,2837],{"className":2836},[647,1475],[580,2838,1451],{"className":2839},[647]," langer Stab in eine Kiste mit ",[580,2842,2844,2882],{"className":2843},[583],[580,2845,2847],{"className":2846},[587],[589,2848,2849],{"xmlns":591},[593,2850,2851,2879],{},[596,2852,2853,2856,2858,2860,2863,2866,2868,2870,2872,2875,2877],{},[611,2854,2855],{},"60",[1446,2857,1448],{},[1446,2859,1451],{},[615,2861,2862],{},"×",[611,2864,2865],{},"40",[1446,2867,1448],{},[1446,2869,1451],{},[615,2871,2862],{},[611,2873,2874],{},"30",[1446,2876,1448],{},[1446,2878,1451],{},[626,2880,2881],{"encoding":628},"60\\,\\text{cm} \\times 40\\,\\text{cm} \\times 30\\,\\text{cm}",[580,2883,2885,2913,2940],{"className":2884,"ariaHidden":634},[633],[580,2886,2888,2892,2895,2898,2904,2907,2910],{"className":2887},[638],[580,2889],{"className":2890,"style":2891},[642],"height:0.7278em;vertical-align:-0.0833em;",[580,2893,2855],{"className":2894},[647],[580,2896],{"className":2897,"style":1471},[718],[580,2899,2901],{"className":2900},[647,1475],[580,2902,1451],{"className":2903},[647],[580,2905],{"className":2906,"style":719},[718],[580,2908,2862],{"className":2909},[723],[580,2911],{"className":2912,"style":719},[718],[580,2914,2916,2919,2922,2925,2931,2934,2937],{"className":2915},[638],[580,2917],{"className":2918,"style":2891},[642],[580,2920,2865],{"className":2921},[647],[580,2923],{"className":2924,"style":1471},[718],[580,2926,2928],{"className":2927},[647,1475],[580,2929,1451],{"className":2930},[647],[580,2932],{"className":2933,"style":719},[718],[580,2935,2862],{"className":2936},[723],[580,2938],{"className":2939,"style":719},[718],[580,2941,2943,2946,2949,2952],{"className":2942},[638],[580,2944],{"className":2945,"style":1464},[642],[580,2947,2874],{"className":2948},[647],[580,2950],{"className":2951,"style":1471},[718],[580,2953,2955],{"className":2954},[647,1475],[580,2956,1451],{"className":2957},[647],"?",[580,2960,2962],{"className":2961},[836],[580,2963,2965,3032],{"className":2964},[583],[580,2966,2968],{"className":2967},[587],[589,2969,2970],{"xmlns":591,"display":845},[593,2971,2972,3029],{},[596,2973,2974,2976,2978,3004,3006,3008,3010,3015,3017,3019,3022,3025,3027],{},[607,2975,1085],{},[615,2977,858],{},[599,2979,2980],{},[596,2981,2982,2988,2990,2996,2998],{},[604,2983,2984,2986],{},[611,2985,2855],{},[611,2987,613],{},[615,2989,617],{},[604,2991,2992,2994],{},[611,2993,2865],{},[611,2995,613],{},[615,2997,617],{},[604,2999,3000,3002],{},[611,3001,2874],{},[611,3003,613],{},[1446,3005,1448],{},[1446,3007,1451],{},[615,3009,858],{},[599,3011,3012],{},[611,3013,3014],{},"6100",[1446,3016,1448],{},[1446,3018,1451],{},[615,3020,3021],{},"≈",[611,3023,3024],{},"78,1",[1446,3026,1448],{},[1446,3028,1451],{},[626,3030,3031],{"encoding":628},"d = \\sqrt{60^2 + 40^2 + 30^2}\\,\\text{cm} = \\sqrt{6100}\\,\\text{cm} \\approx 78{,}1\\,\\text{cm}",[580,3033,3035,3053,3236,3307],{"className":3034,"ariaHidden":634},[633],[580,3036,3038,3041,3044,3047,3050],{"className":3037},[638],[580,3039],{"className":3040,"style":1097},[642],[580,3042,1085],{"className":3043},[647,683],[580,3045],{"className":3046,"style":920},[718],[580,3048,858],{"className":3049},[924],[580,3051],{"className":3052,"style":920},[718],[580,3054,3056,3059,3218,3221,3227,3230,3233],{"className":3055},[638],[580,3057],{"className":3058,"style":1689},[642],[580,3060,3062],{"className":3061},[647,648],[580,3063,3065,3210],{"className":3064},[652,653],[580,3066,3068,3207],{"className":3067},[657],[580,3069,3071,3195],{"className":3070,"style":1702},[661],[580,3072,3074,3077],{"className":3073,"style":1706},[666],[580,3075],{"className":3076,"style":1710},[671],[580,3078,3080,3083,3113,3116,3119,3122,3125,3154,3157,3160,3163,3166],{"className":3079,"style":1714},[647],[580,3081,1538],{"className":3082},[647],[580,3084,3086,3090],{"className":3085},[647],[580,3087,3089],{"className":3088},[647],"0",[580,3091,3093],{"className":3092},[687],[580,3094,3096],{"className":3095},[652],[580,3097,3099],{"className":3098},[657],[580,3100,3102],{"className":3101,"style":697},[661],[580,3103,3104,3107],{"style":700},[580,3105],{"className":3106,"style":704},[671],[580,3108,3110],{"className":3109},[708,709,710,711],[580,3111,613],{"className":3112},[647,711],[580,3114],{"className":3115,"style":719},[718],[580,3117,617],{"className":3118},[723],[580,3120],{"className":3121,"style":719},[718],[580,3123,1624],{"className":3124},[647],[580,3126,3128,3131],{"className":3127},[647],[580,3129,3089],{"className":3130},[647],[580,3132,3134],{"className":3133},[687],[580,3135,3137],{"className":3136},[652],[580,3138,3140],{"className":3139},[657],[580,3141,3143],{"className":3142,"style":697},[661],[580,3144,3145,3148],{"style":700},[580,3146],{"className":3147,"style":704},[671],[580,3149,3151],{"className":3150},[708,709,710,711],[580,3152,613],{"className":3153},[647,711],[580,3155],{"className":3156,"style":719},[718],[580,3158,617],{"className":3159},[723],[580,3161],{"className":3162,"style":719},[718],[580,3164,1494],{"className":3165},[647],[580,3167,3169,3172],{"className":3168},[647],[580,3170,3089],{"className":3171},[647],[580,3173,3175],{"className":3174},[687],[580,3176,3178],{"className":3177},[652],[580,3179,3181],{"className":3180},[657],[580,3182,3184],{"className":3183,"style":697},[661],[580,3185,3186,3189],{"style":700},[580,3187],{"className":3188,"style":704},[671],[580,3190,3192],{"className":3191},[708,709,710,711],[580,3193,613],{"className":3194},[647,711],[580,3196,3197,3200],{"style":1822},[580,3198],{"className":3199,"style":1710},[671],[580,3201,3203],{"className":3202,"style":1829},[765],[768,3204,3205],{"xmlns":770,"width":771,"height":1832,"viewBox":1833,"preserveAspectRatio":774},[776,3206],{"d":1836},[580,3208,783],{"className":3209},[782],[580,3211,3213],{"className":3212},[657],[580,3214,3216],{"className":3215,"style":1846},[661],[580,3217],{},[580,3219],{"className":3220,"style":1471},[718],[580,3222,3224],{"className":3223},[647,1475],[580,3225,1451],{"className":3226},[647],[580,3228],{"className":3229,"style":920},[718],[580,3231,858],{"className":3232},[924],[580,3234],{"className":3235,"style":920},[718],[580,3237,3239,3242,3289,3292,3298,3301,3304],{"className":3238},[638],[580,3240],{"className":3241,"style":1972},[642],[580,3243,3245],{"className":3244},[647,648],[580,3246,3248,3281],{"className":3247},[652,653],[580,3249,3251,3278],{"className":3250},[657],[580,3252,3254,3266],{"className":3253,"style":1985},[661],[580,3255,3257,3260],{"className":3256,"style":667},[666],[580,3258],{"className":3259,"style":672},[671],[580,3261,3263],{"className":3262,"style":676},[647],[580,3264,3014],{"className":3265},[647],[580,3267,3268,3271],{"style":2000},[580,3269],{"className":3270,"style":672},[671],[580,3272,3274],{"className":3273,"style":766},[765],[768,3275,3276],{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},[776,3277],{"d":778},[580,3279,783],{"className":3280},[782],[580,3282,3284],{"className":3283},[657],[580,3285,3287],{"className":3286,"style":2020},[661],[580,3288],{},[580,3290],{"className":3291,"style":1471},[718],[580,3293,3295],{"className":3294},[647,1475],[580,3296,1451],{"className":3297},[647],[580,3299],{"className":3300,"style":920},[718],[580,3302,3021],{"className":3303},[924],[580,3305],{"className":3306,"style":920},[718],[580,3308,3310,3314,3318,3326,3329,3332],{"className":3309},[638],[580,3311],{"className":3312,"style":3313},[642],"height:0.8389em;vertical-align:-0.1944em;",[580,3315,3317],{"className":3316},[647],"78",[580,3319,3321],{"className":3320},[647],[580,3322,3325],{"className":3323},[3324],"mpunct",",",[580,3327,2634],{"className":3328},[647],[580,3330],{"className":3331,"style":1471},[718],[580,3333,3335],{"className":3334},[647,1475],[580,3336,1451],{"className":3337},[647],[564,3339,3340],{},"Ja, schräg durch die Kiste passt er hinein.",[559,3342,3344],{"id":3343},"typische-fehler","Typische Fehler",[3346,3347,3348,3352,3522],"ul",{},[3349,3350,3351],"li",{},"Flächendiagonale und Raumdiagonale verwechseln. Die Raumdiagonale braucht alle drei Kanten.",[3349,3353,3354,3355,3521],{},"Im zweiten Schritt mit einer gerundeten Flächendiagonale weiterrechnen. Das erzeugt Rundungsfehler; besser gleich ",[580,3356,3358,3392],{"className":3357},[583],[580,3359,3361],{"className":3360},[587],[589,3362,3363],{"xmlns":591},[593,3364,3365,3389],{},[596,3366,3367,3373,3375,3381,3383],{},[604,3368,3369,3371],{},[607,3370,609],{},[611,3372,613],{},[615,3374,617],{},[604,3376,3377,3379],{},[607,3378,622],{},[611,3380,613],{},[615,3382,617],{},[604,3384,3385,3387],{},[607,3386,1054],{},[611,3388,613],{},[626,3390,3391],{"encoding":628},"a^2 + b^2 + c^2",[580,3393,3395,3442,3486],{"className":3394,"ariaHidden":634},[633],[580,3396,3398,3402,3433,3436,3439],{"className":3397},[638],[580,3399],{"className":3400,"style":3401},[642],"height:0.8974em;vertical-align:-0.0833em;",[580,3403,3405,3408],{"className":3404},[647],[580,3406,609],{"className":3407},[647,683],[580,3409,3411],{"className":3410},[687],[580,3412,3414],{"className":3413},[652],[580,3415,3417],{"className":3416},[657],[580,3418,3421],{"className":3419,"style":3420},[661],"height:0.8141em;",[580,3422,3424,3427],{"style":3423},"top:-3.063em;margin-right:0.05em;",[580,3425],{"className":3426,"style":704},[671],[580,3428,3430],{"className":3429},[708,709,710,711],[580,3431,613],{"className":3432},[647,711],[580,3434],{"className":3435,"style":719},[718],[580,3437,617],{"className":3438},[723],[580,3440],{"className":3441,"style":719},[718],[580,3443,3445,3448,3477,3480,3483],{"className":3444},[638],[580,3446],{"className":3447,"style":3401},[642],[580,3449,3451,3454],{"className":3450},[647],[580,3452,622],{"className":3453},[647,683],[580,3455,3457],{"className":3456},[687],[580,3458,3460],{"className":3459},[652],[580,3461,3463],{"className":3462},[657],[580,3464,3466],{"className":3465,"style":3420},[661],[580,3467,3468,3471],{"style":3423},[580,3469],{"className":3470,"style":704},[671],[580,3472,3474],{"className":3473},[708,709,710,711],[580,3475,613],{"className":3476},[647,711],[580,3478],{"className":3479,"style":719},[718],[580,3481,617],{"className":3482},[723],[580,3484],{"className":3485,"style":719},[718],[580,3487,3489,3492],{"className":3488},[638],[580,3490],{"className":3491,"style":3420},[642],[580,3493,3495,3498],{"className":3494},[647],[580,3496,1054],{"className":3497},[647,683],[580,3499,3501],{"className":3500},[687],[580,3502,3504],{"className":3503},[652],[580,3505,3507],{"className":3506},[657],[580,3508,3510],{"className":3509,"style":3420},[661],[580,3511,3512,3515],{"style":3423},[580,3513],{"className":3514,"style":704},[671],[580,3516,3518],{"className":3517},[708,709,710,711],[580,3519,613],{"className":3520},[647,711]," addieren und erst am Ende die Wurzel ziehen.",[3349,3523,3524,3525,3835],{},"Die Wurzel auf die Summanden verteilen: ",[580,3526,3528,3580],{"className":3527},[583],[580,3529,3531],{"className":3530},[587],[589,3532,3533],{"xmlns":591},[593,3534,3535,3577],{},[596,3536,3537,3563,3567,3569,3571,3573,3575],{},[599,3538,3539],{},[596,3540,3541,3547,3549,3555,3557],{},[604,3542,3543,3545],{},[607,3544,609],{},[611,3546,613],{},[615,3548,617],{},[604,3550,3551,3553],{},[607,3552,622],{},[611,3554,613],{},[615,3556,617],{},[604,3558,3559,3561],{},[607,3560,1054],{},[611,3562,613],{},[615,3564,3566],{"mathvariant":3565},"normal","≠",[607,3568,609],{},[615,3570,617],{},[607,3572,622],{},[615,3574,617],{},[607,3576,1054],{},[626,3578,3579],{"encoding":628},"\\sqrt{a^2 + b^2 + c^2} \\neq a + b + c",[580,3581,3583,3788,3807,3826],{"className":3582,"ariaHidden":634},[633],[580,3584,3586,3590,3739,3742,3785],{"className":3585},[638],[580,3587],{"className":3588,"style":3589},[642],"height:1.1078em;vertical-align:-0.1944em;",[580,3591,3593],{"className":3592},[647,648],[580,3594,3596,3731],{"className":3595},[652,653],[580,3597,3599,3728],{"className":3598},[657],[580,3600,3602,3716],{"className":3601,"style":662},[661],[580,3603,3605,3608],{"className":3604,"style":667},[666],[580,3606],{"className":3607,"style":672},[671],[580,3609,3611,3640,3643,3646,3649,3678,3681,3684,3687],{"className":3610,"style":676},[647],[580,3612,3614,3617],{"className":3613},[647],[580,3615,609],{"className":3616},[647,683],[580,3618,3620],{"className":3619},[687],[580,3621,3623],{"className":3622},[652],[580,3624,3626],{"className":3625},[657],[580,3627,3629],{"className":3628,"style":697},[661],[580,3630,3631,3634],{"style":700},[580,3632],{"className":3633,"style":704},[671],[580,3635,3637],{"className":3636},[708,709,710,711],[580,3638,613],{"className":3639},[647,711],[580,3641],{"className":3642,"style":719},[718],[580,3644,617],{"className":3645},[723],[580,3647],{"className":3648,"style":719},[718],[580,3650,3652,3655],{"className":3651},[647],[580,3653,622],{"className":3654},[647,683],[580,3656,3658],{"className":3657},[687],[580,3659,3661],{"className":3660},[652],[580,3662,3664],{"className":3663},[657],[580,3665,3667],{"className":3666,"style":697},[661],[580,3668,3669,3672],{"style":700},[580,3670],{"className":3671,"style":704},[671],[580,3673,3675],{"className":3674},[708,709,710,711],[580,3676,613],{"className":3677},[647,711],[580,3679],{"className":3680,"style":719},[718],[580,3682,617],{"className":3683},[723],[580,3685],{"className":3686,"style":719},[718],[580,3688,3690,3693],{"className":3689},[647],[580,3691,1054],{"className":3692},[647,683],[580,3694,3696],{"className":3695},[687],[580,3697,3699],{"className":3698},[652],[580,3700,3702],{"className":3701},[657],[580,3703,3705],{"className":3704,"style":697},[661],[580,3706,3707,3710],{"style":700},[580,3708],{"className":3709,"style":704},[671],[580,3711,3713],{"className":3712},[708,709,710,711],[580,3714,613],{"className":3715},[647,711],[580,3717,3718,3721],{"style":758},[580,3719],{"className":3720,"style":672},[671],[580,3722,3724],{"className":3723,"style":766},[765],[768,3725,3726],{"xmlns":770,"width":771,"height":772,"viewBox":773,"preserveAspectRatio":774},[776,3727],{"d":778},[580,3729,783],{"className":3730},[782],[580,3732,3734],{"className":3733},[657],[580,3735,3737],{"className":3736,"style":790},[661],[580,3738],{},[580,3740],{"className":3741,"style":920},[718],[580,3743,3745,3778,3782],{"className":3744},[924],[580,3746,3748],{"className":3747},[924],[580,3749,3752],{"className":3750},[647,3751],"vbox",[580,3753,3756],{"className":3754},[3755],"thinbox",[580,3757,3760,3763,3774],{"className":3758},[3759],"rlap",[580,3761],{"className":3762,"style":827},[642],[580,3764,3767],{"className":3765},[3766],"inner",[580,3768,3770],{"className":3769},[647],[580,3771,3773],{"className":3772},[924],"",[580,3775],{"className":3776},[3777],"fix",[580,3779],{"className":3780},[718,3781],"nobreak",[580,3783,858],{"className":3784},[924],[580,3786],{"className":3787,"style":920},[718],[580,3789,3791,3795,3798,3801,3804],{"className":3790},[638],[580,3792],{"className":3793,"style":3794},[642],"height:0.6667em;vertical-align:-0.0833em;",[580,3796,609],{"className":3797},[647,683],[580,3799],{"className":3800,"style":719},[718],[580,3802,617],{"className":3803},[723],[580,3805],{"className":3806,"style":719},[718],[580,3808,3810,3814,3817,3820,3823],{"className":3809},[638],[580,3811],{"className":3812,"style":3813},[642],"height:0.7778em;vertical-align:-0.0833em;",[580,3815,622],{"className":3816},[647,683],[580,3818],{"className":3819,"style":719},[718],[580,3821,617],{"className":3822},[723],[580,3824],{"className":3825,"style":719},[718],[580,3827,3829,3832],{"className":3828},[638],[580,3830],{"className":3831,"style":1066},[642],[580,3833,1054],{"className":3834},[647,683],".",{"title":3837,"searchDepth":3838,"depth":3838,"links":3839},"",2,[3840,3841,3842,3843],{"id":561,"depth":3838,"text":562},{"id":796,"depth":3838,"text":797},{"id":1426,"depth":3838,"text":1427},{"id":3343,"depth":3838,"text":3344},[3845,3848,3851,3853,3855,3857,3859,3862],{"lhs":3846,"rhs":3847},"sqrt(sqrt(a^2 + b^2)^2 + c^2)","sqrt(a^2 + b^2 + c^2)",{"lhs":3849,"rhs":3850},"sqrt(a^2 + a^2 + a^2)","a*sqrt(3)",{"lhs":3852,"rhs":1654},"sqrt(2^2 + 3^2 + 6^2)",{"lhs":3854,"rhs":2298},"sqrt(4^2 + 3^2)",{"lhs":3856,"rhs":2537},"sqrt(5^2 + 12^2)",{"lhs":3858,"rhs":2537},"sqrt(4^2 + 3^2 + 12^2)",{"lhs":3860,"rhs":3861},"sqrt(60^2 + 40^2 + 30^2)","sqrt(6100)",{"lhs":3863,"rhs":3864},"round(sqrt(6100), 1)","78.1","a > 0,\\ b > 0,\\ c > 0","\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>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a > 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:0.5782em;vertical-align:-0.0391em;\">\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: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>b\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b > 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:0.7335em;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:0.8389em;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>c\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.5782em;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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3870,"x":3871,"y":3874,"items":3877},"Quader mit Länge a, Breite b und Höhe c; Flächendiagonale f und Raumdiagonale d bilden mit c ein rechtwinkliges Dreieck",[3872,3873],-0.6,4.6,[3875,3876],-0.65,2.95,[3878,3885,3889,3892,3895,3900,3904,3908,3911,3914,3918,3921,3924,3931,3934,3939,3944,3948,3952,3956],{"type":3879,"from":3880,"to":3882,"style":3884},"segment",[3881,3881],0,[3883,3881],3,"muted",{"type":3879,"from":3886,"to":3887,"style":3884},[3883,3881],[3883,3888],1.8,{"type":3879,"from":3890,"to":3891,"style":3884},[3883,3888],[3881,3888],{"type":3879,"from":3893,"to":3894,"style":3884},[3881,3888],[3881,3881],{"type":3879,"from":3896,"to":3897,"style":3884},[3883,3881],[3898,3899],4,0.7,{"type":3879,"from":3901,"to":3902,"style":3884},[3883,3888],[3898,3903],2.5,{"type":3879,"from":3905,"to":3906,"style":3884},[3881,3888],[3907,3903],1,{"type":3879,"from":3909,"to":3910,"style":3884},[3898,3899],[3898,3903],{"type":3879,"from":3912,"to":3913,"style":3884},[3898,3903],[3907,3903],{"type":3879,"from":3915,"to":3916,"style":3917},[3907,3899],[3881,3881],"dashed",{"type":3879,"from":3919,"to":3920,"style":3917},[3907,3899],[3898,3899],{"type":3879,"from":3922,"to":3923,"style":3917},[3907,3899],[3907,3903],{"type":3925,"points":3926,"fill":3930,"style":3917},"polygon",[3927,3928,3929],[3881,3881],[3898,3899],[3898,3903],true,{"type":3879,"from":3932,"to":3933},[3881,3881],[3898,3903],{"type":3935,"at":3936,"from":3937,"to":3938},"rightAngle",[3898,3899],[3881,3881],[3898,3903],{"type":3940,"at":3941,"text":609},"label",[3942,3943],1.5,-0.35,{"type":3940,"at":3945,"text":622},[3946,3947],3.85,0.25,{"type":3940,"at":3949,"text":1054},[3950,3951],4.3,1.6,{"type":3940,"at":3953,"text":815},[3954,3955],2.3,0.3,{"type":3940,"at":3957,"text":1085},[3958,3959],1.7,1.45,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 172.8\" width=\"249.6\" height=\"172.8\" role=\"img\" aria-label=\"Quader mit Länge a, Breite b und Höhe c; Flächendiagonale f und Raumdiagonale d bilden mit c ein rechtwinkliges Dreieck\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-cuboid-space-diagonal-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-cuboid-space-diagonal-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"172.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"28.8\" y1=\"141.6\" x2=\"172.8\" y2=\"141.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"172.8\" y1=\"141.6\" x2=\"172.8\" y2=\"55.2\" class=\"fig-muted\"\u002F>\u003Cline x1=\"172.8\" y1=\"55.2\" x2=\"28.8\" y2=\"55.2\" class=\"fig-muted\"\u002F>\u003Cline x1=\"28.8\" y1=\"55.2\" x2=\"28.8\" y2=\"141.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"172.8\" y1=\"141.6\" x2=\"220.8\" y2=\"108\" class=\"fig-muted\"\u002F>\u003Cline x1=\"172.8\" y1=\"55.2\" x2=\"220.8\" y2=\"21.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"28.8\" y1=\"55.2\" x2=\"76.8\" y2=\"21.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"220.8\" y1=\"108\" x2=\"220.8\" y2=\"21.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"220.8\" y1=\"21.6\" x2=\"76.8\" y2=\"21.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"76.8\" y1=\"108\" x2=\"28.8\" y2=\"141.6\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"76.8\" y1=\"108\" x2=\"220.8\" y2=\"108\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"76.8\" y1=\"108\" x2=\"76.8\" y2=\"21.6\" class=\"fig-dashed\"\u002F>\u003Cpolygon points=\"28.8,141.6 220.8,108 220.8,21.6\" class=\"fig-dashed fig-fill\"\u002F>\u003Cline x1=\"28.8\" y1=\"141.6\" x2=\"220.8\" y2=\"21.6\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 208.98 110.07 L 208.98 98.07 L 220.8 96\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"214.89\" cy=\"103.03\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"100.8\" y=\"158.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"213.6\" y=\"129.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"235.2\" y=\"64.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ctext x=\"139.2\" y=\"127.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003Ctext x=\"110.4\" y=\"72\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">d\u003C\u002Ftext>\u003C\u002Fsvg>","cuboid-space-diagonal","d = \\sqrt{a^2 + b^2 + c^2}","\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>d\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d = \\sqrt{a^2 + b^2 + c^2}\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\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:1.24em;vertical-align:-0.1777em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.0623em;\">\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\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.0223em;\">\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:0.1777em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fraumdiagonale-quader",[],[3969,3970,3971,3972],"rectangle-diagonal","cube-space-diagonal","pythagorean-theorem","cuboid-volume",{"title":548,"description":3837},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fraumdiagonale-quader","Die Raumdiagonale eines Quaders ist die Wurzel aus der Summe der Quadrate von Länge, Breite und Höhe.",[3977,3978,3979,3980],"raumdiagonale","quader","pythagoras","körper",[3982,3985],{"symbol":1085,"meaning":3983,"symbolHtml":3984},"Länge der Raumdiagonale, der Strecke zwischen zwei gegenüberliegenden Ecken durch das Innere","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3986,"meaning":3987,"symbolHtml":3988},"a, b, c","Länge, Breite und Höhe des Quaders","\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>","RjOn0t_mr5d72pDffy7qp2Z9GOW_tgRmQDJ5xgpdp34",[3991,3994,3997,4000],{"stem":3992,"title":3993,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fdiagonale-rechteck","Diagonale eines Rechtecks",{"stem":3995,"title":3996,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fraumdiagonale-wuerfel","Raumdiagonale eines Würfels",{"stem":3998,"title":3999,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des Pythagoras",{"stem":4001,"title":4002,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-quader","Volumen eines Quaders",1793824269719]