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Die Grundfläche ist ein Vieleck, z.B. ein Dreieck oder Sechseck. Die Seitenflächen sind Rechtecke (beim geraden Prisma) oder Parallelogramme (beim schiefen Prisma).",[564,581,582,583,629,630,633],{},"Das Volumen ist immer Grundfläche mal Höhe. Die Höhe ",[584,585,588,610],"span",{"className":586},[587],"katex",[584,589,592],{"className":590},[591],"katex-mathml",[593,594,596],"math",{"xmlns":595},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[597,598,599,606],"semantics",{},[600,601,602],"mrow",{},[603,604,605],"mi",{},"h",[607,608,605],"annotation",{"encoding":609},"application\u002Fx-tex",[584,611,615],{"className":612,"ariaHidden":614},[613],"katex-html","true",[584,616,619,624],{"className":617},[618],"base",[584,620],{"className":621,"style":623},[622],"strut","height:0.6944em;",[584,625,605],{"className":626},[627,628],"mord","mathnormal"," ist der ",[568,631,632],{},"senkrechte"," Abstand zwischen Grund- und Deckfläche, bei einem schiefen Prisma also nicht die Länge der schrägen Kante.",[564,635,636,637,723,724,822],{},"Der Quader ist ein Prisma mit rechteckiger Grundfläche: ",[584,638,640,668],{"className":639},[587],[584,641,643],{"className":642},[591],[593,644,645],{"xmlns":595},[597,646,647,665],{},[600,648,649,652,656,659,662],{},[603,650,651],{},"G",[653,654,655],"mo",{},"=",[603,657,658],{},"a",[653,660,661],{},"⋅",[603,663,664],{},"b",[607,666,667],{"encoding":609},"G = a \\cdot b",[584,669,671,693,714],{"className":670,"ariaHidden":614},[613],[584,672,674,678,681,686,690],{"className":673},[618],[584,675],{"className":676,"style":677},[622],"height:0.6833em;",[584,679,651],{"className":680},[627,628],[584,682],{"className":683,"style":685},[684],"mspace","margin-right:0.2778em;",[584,687,655],{"className":688},[689],"mrel",[584,691],{"className":692,"style":685},[684],[584,694,696,700,703,707,711],{"className":695},[618],[584,697],{"className":698,"style":699},[622],"height:0.4445em;",[584,701,658],{"className":702},[627,628],[584,704],{"className":705,"style":706},[684],"margin-right:0.2222em;",[584,708,661],{"className":709},[710],"mbin",[584,712],{"className":713,"style":706},[684],[584,715,717,720],{"className":716},[618],[584,718],{"className":719,"style":623},[622],[584,721,664],{"className":722},[627,628],", also ",[584,725,727,755],{"className":726},[587],[584,728,730],{"className":729},[591],[593,731,732],{"xmlns":595},[597,733,734,752],{},[600,735,736,739,741,743,745,747,749],{},[603,737,738],{},"V",[653,740,655],{},[603,742,658],{},[653,744,661],{},[603,746,664],{},[653,748,661],{},[603,750,751],{},"c",[607,753,754],{"encoding":609},"V = a \\cdot b \\cdot c",[584,756,758,776,794,812],{"className":757,"ariaHidden":614},[613],[584,759,761,764,767,770,773],{"className":760},[618],[584,762],{"className":763,"style":677},[622],[584,765,738],{"className":766,"style":706},[627,628],[584,768],{"className":769,"style":685},[684],[584,771,655],{"className":772},[689],[584,774],{"className":775,"style":685},[684],[584,777,779,782,785,788,791],{"className":778},[618],[584,780],{"className":781,"style":699},[622],[584,783,658],{"className":784},[627,628],[584,786],{"className":787,"style":706},[684],[584,789,661],{"className":790},[710],[584,792],{"className":793,"style":706},[684],[584,795,797,800,803,806,809],{"className":796},[618],[584,798],{"className":799,"style":623},[622],[584,801,664],{"className":802},[627,628],[584,804],{"className":805,"style":706},[684],[584,807,661],{"className":808},[710],[584,810],{"className":811,"style":706},[684],[584,813,815,819],{"className":814},[618],[584,816],{"className":817,"style":818},[622],"height:0.4306em;",[584,820,751],{"className":821},[627,628],".",[564,824,825,826,854,855,822],{},"Zuerst berechnet man ",[584,827,829,842],{"className":828},[587],[584,830,832],{"className":831},[591],[593,833,834],{"xmlns":595},[597,835,836,840],{},[600,837,838],{},[603,839,651],{},[607,841,651],{"encoding":609},[584,843,845],{"className":844,"ariaHidden":614},[613],[584,846,848,851],{"className":847},[618],[584,849],{"className":850,"style":677},[622],[584,852,651],{"className":853},[627,628]," mit der passenden Flächenformel, dann multipliziert man mit ",[584,856,858,871],{"className":857},[587],[584,859,861],{"className":860},[591],[593,862,863],{"xmlns":595},[597,864,865,869],{},[600,866,867],{},[603,868,605],{},[607,870,605],{"encoding":609},[584,872,874],{"className":873,"ariaHidden":614},[613],[584,875,877,880],{"className":876},[618],[584,878],{"className":879,"style":623},[622],[584,881,605],{"className":882},[627,628],[559,884,886],{"id":885},"beispiele","Beispiele",[564,888,889,890,940,941,984,985,1028],{},"Ein Prisma hat ein Dreieck als Grundfläche. Das Dreieck hat die Grundseite ",[584,891,893,916],{"className":892},[587],[584,894,896],{"className":895},[591],[593,897,898],{"xmlns":595},[597,899,900,913],{},[600,901,902,906,910],{},[903,904,905],"mn",{},"4",[907,908,909],"mtext",{}," ",[907,911,912],{},"cm",[607,914,915],{"encoding":609},"4\\,\\text{cm}",[584,917,919],{"className":918,"ariaHidden":614},[613],[584,920,922,926,929,933],{"className":921},[618],[584,923],{"className":924,"style":925},[622],"height:0.6444em;",[584,927,905],{"className":928},[627],[584,930],{"className":931,"style":932},[684],"margin-right:0.1667em;",[584,934,937],{"className":935},[627,936],"text",[584,938,912],{"className":939},[627]," und die Höhe ",[584,942,944,963],{"className":943},[587],[584,945,947],{"className":946},[591],[593,948,949],{"xmlns":595},[597,950,951,960],{},[600,952,953,956,958],{},[903,954,955],{},"3",[907,957,909],{},[907,959,912],{},[607,961,962],{"encoding":609},"3\\,\\text{cm}",[584,964,966],{"className":965,"ariaHidden":614},[613],[584,967,969,972,975,978],{"className":968},[618],[584,970],{"className":971,"style":925},[622],[584,973,955],{"className":974},[627],[584,976],{"className":977,"style":932},[684],[584,979,981],{"className":980},[627,936],[584,982,912],{"className":983},[627],". Das Prisma ist ",[584,986,988,1007],{"className":987},[587],[584,989,991],{"className":990},[591],[593,992,993],{"xmlns":595},[597,994,995,1004],{},[600,996,997,1000,1002],{},[903,998,999],{},"10",[907,1001,909],{},[907,1003,912],{},[607,1005,1006],{"encoding":609},"10\\,\\text{cm}",[584,1008,1010],{"className":1009,"ariaHidden":614},[613],[584,1011,1013,1016,1019,1022],{"className":1012},[618],[584,1014],{"className":1015,"style":925},[622],[584,1017,999],{"className":1018},[627],[584,1020],{"className":1021,"style":932},[684],[584,1023,1025],{"className":1024},[627,936],[584,1026,912],{"className":1027},[627]," hoch:",[584,1030,1033],{"className":1031},[1032],"katex-display",[584,1034,1036,1130],{"className":1035},[587],[584,1037,1039],{"className":1038},[591],[593,1040,1042],{"xmlns":595,"display":1041},"block",[597,1043,1044,1127],{},[600,1045,1046,1048,1050,1059,1061,1063,1065,1067,1069,1071,1073,1075,1077,1080,1082,1089,1092,1094,1096,1098,1100,1106,1108,1110,1112,1114,1116,1119,1121],{},[603,1047,651],{},[653,1049,655],{},[1051,1052,1053,1056],"mfrac",{},[903,1054,1055],{},"1",[903,1057,1058],{},"2",[653,1060,661],{},[903,1062,905],{},[907,1064,909],{},[907,1066,912],{},[653,1068,661],{},[903,1070,955],{},[907,1072,909],{},[907,1074,912],{},[653,1076,655],{},[903,1078,1079],{},"6",[907,1081,909],{},[1083,1084,1085,1087],"msup",{},[907,1086,912],{},[903,1088,1058],{},[684,1090],{"width":1091},"2em",[603,1093,738],{},[653,1095,655],{},[903,1097,1079],{},[907,1099,909],{},[1083,1101,1102,1104],{},[907,1103,912],{},[903,1105,1058],{},[653,1107,661],{},[903,1109,999],{},[907,1111,909],{},[907,1113,912],{},[653,1115,655],{},[903,1117,1118],{},"60",[907,1120,909],{},[1083,1122,1123,1125],{},[907,1124,912],{},[903,1126,955],{},[607,1128,1129],{"encoding":609},"G = \\frac{1}{2} \\cdot 4\\,\\text{cm} \\cdot 3\\,\\text{cm} = 6\\,\\text{cm}^2\n\\qquad\nV = 6\\,\\text{cm}^2 \\cdot 10\\,\\text{cm} = 60\\,\\text{cm}^3",[584,1131,1133,1151,1247,1274,1301,1369,1422,1449],{"className":1132,"ariaHidden":614},[613],[584,1134,1136,1139,1142,1145,1148],{"className":1135},[618],[584,1137],{"className":1138,"style":677},[622],[584,1140,651],{"className":1141},[627,628],[584,1143],{"className":1144,"style":685},[684],[584,1146,655],{"className":1147},[689],[584,1149],{"className":1150,"style":685},[684],[584,1152,1154,1158,1238,1241,1244],{"className":1153},[618],[584,1155],{"className":1156,"style":1157},[622],"height:2.0074em;vertical-align:-0.686em;",[584,1159,1161,1166,1234],{"className":1160},[627],[584,1162],{"className":1163},[1164,1165],"mopen","nulldelimiter",[584,1167,1169],{"className":1168},[1051],[584,1170,1174,1225],{"className":1171},[1172,1173],"vlist-t","vlist-t2",[584,1175,1178,1220],{"className":1176},[1177],"vlist-r",[584,1179,1183,1197,1208],{"className":1180,"style":1182},[1181],"vlist","height:1.3214em;",[584,1184,1186,1191],{"style":1185},"top:-2.314em;",[584,1187],{"className":1188,"style":1190},[1189],"pstrut","height:3em;",[584,1192,1194],{"className":1193},[627],[584,1195,1058],{"className":1196},[627],[584,1198,1200,1203],{"style":1199},"top:-3.23em;",[584,1201],{"className":1202,"style":1190},[1189],[584,1204],{"className":1205,"style":1207},[1206],"frac-line","border-bottom-width:0.04em;",[584,1209,1211,1214],{"style":1210},"top:-3.677em;",[584,1212],{"className":1213,"style":1190},[1189],[584,1215,1217],{"className":1216},[627],[584,1218,1055],{"className":1219},[627],[584,1221,1224],{"className":1222},[1223],"vlist-s","​",[584,1226,1228],{"className":1227},[1177],[584,1229,1232],{"className":1230,"style":1231},[1181],"height:0.686em;",[584,1233],{},[584,1235],{"className":1236},[1237,1165],"mclose",[584,1239],{"className":1240,"style":706},[684],[584,1242,661],{"className":1243},[710],[584,1245],{"className":1246,"style":706},[684],[584,1248,1250,1253,1256,1259,1265,1268,1271],{"className":1249},[618],[584,1251],{"className":1252,"style":925},[622],[584,1254,905],{"className":1255},[627],[584,1257],{"className":1258,"style":932},[684],[584,1260,1262],{"className":1261},[627,936],[584,1263,912],{"className":1264},[627],[584,1266],{"className":1267,"style":706},[684],[584,1269,661],{"className":1270},[710],[584,1272],{"className":1273,"style":706},[684],[584,1275,1277,1280,1283,1286,1292,1295,1298],{"className":1276},[618],[584,1278],{"className":1279,"style":925},[622],[584,1281,955],{"className":1282},[627],[584,1284],{"className":1285,"style":932},[684],[584,1287,1289],{"className":1288},[627,936],[584,1290,912],{"className":1291},[627],[584,1293],{"className":1294,"style":685},[684],[584,1296,655],{"className":1297},[689],[584,1299],{"className":1300,"style":685},[684],[584,1302,1304,1308,1311,1314,1353,1357,1360,1363,1366],{"className":1303},[618],[584,1305],{"className":1306,"style":1307},[622],"height:0.8641em;",[584,1309,1079],{"className":1310},[627],[584,1312],{"className":1313,"style":932},[684],[584,1315,1317,1323],{"className":1316},[627],[584,1318,1320],{"className":1319},[627,936],[584,1321,912],{"className":1322},[627],[584,1324,1327],{"className":1325},[1326],"msupsub",[584,1328,1330],{"className":1329},[1172],[584,1331,1333],{"className":1332},[1177],[584,1334,1336],{"className":1335,"style":1307},[1181],[584,1337,1339,1343],{"style":1338},"top:-3.113em;margin-right:0.05em;",[584,1340],{"className":1341,"style":1342},[1189],"height:2.7em;",[584,1344,1350],{"className":1345},[1346,1347,1348,1349],"sizing","reset-size6","size3","mtight",[584,1351,1058],{"className":1352},[627,1349],[584,1354],{"className":1355,"style":1356},[684],"margin-right:2em;",[584,1358,738],{"className":1359,"style":706},[627,628],[584,1361],{"className":1362,"style":685},[684],[584,1364,655],{"className":1365},[689],[584,1367],{"className":1368,"style":685},[684],[584,1370,1372,1375,1378,1381,1413,1416,1419],{"className":1371},[618],[584,1373],{"className":1374,"style":1307},[622],[584,1376,1079],{"className":1377},[627],[584,1379],{"className":1380,"style":932},[684],[584,1382,1384,1390],{"className":1383},[627],[584,1385,1387],{"className":1386},[627,936],[584,1388,912],{"className":1389},[627],[584,1391,1393],{"className":1392},[1326],[584,1394,1396],{"className":1395},[1172],[584,1397,1399],{"className":1398},[1177],[584,1400,1402],{"className":1401,"style":1307},[1181],[584,1403,1404,1407],{"style":1338},[584,1405],{"className":1406,"style":1342},[1189],[584,1408,1410],{"className":1409},[1346,1347,1348,1349],[584,1411,1058],{"className":1412},[627,1349],[584,1414],{"className":1415,"style":706},[684],[584,1417,661],{"className":1418},[710],[584,1420],{"className":1421,"style":706},[684],[584,1423,1425,1428,1431,1434,1440,1443,1446],{"className":1424},[618],[584,1426],{"className":1427,"style":925},[622],[584,1429,999],{"className":1430},[627],[584,1432],{"className":1433,"style":932},[684],[584,1435,1437],{"className":1436},[627,936],[584,1438,912],{"className":1439},[627],[584,1441],{"className":1442,"style":685},[684],[584,1444,655],{"className":1445},[689],[584,1447],{"className":1448,"style":685},[684],[584,1450,1452,1455,1458,1461],{"className":1451},[618],[584,1453],{"className":1454,"style":1307},[622],[584,1456,1118],{"className":1457},[627],[584,1459],{"className":1460,"style":932},[684],[584,1462,1464,1470],{"className":1463},[627],[584,1465,1467],{"className":1466},[627,936],[584,1468,912],{"className":1469},[627],[584,1471,1473],{"className":1472},[1326],[584,1474,1476],{"className":1475},[1172],[584,1477,1479],{"className":1478},[1177],[584,1480,1482],{"className":1481,"style":1307},[1181],[584,1483,1484,1487],{"style":1338},[584,1485],{"className":1486,"style":1342},[1189],[584,1488,1490],{"className":1489},[1346,1347,1348,1349],[584,1491,955],{"className":1492},[627,1349],[564,1494,1495,1496,1539,1540,1582,1583,1625,1626,1669],{},"Ein Wassergraben hat einen trapezförmigen Querschnitt: oben ",[584,1497,1499,1518],{"className":1498},[587],[584,1500,1502],{"className":1501},[591],[593,1503,1504],{"xmlns":595},[597,1505,1506,1515],{},[600,1507,1508,1510,1512],{},[903,1509,1079],{},[907,1511,909],{},[907,1513,1514],{},"m",[607,1516,1517],{"encoding":609},"6\\,\\text{m}",[584,1519,1521],{"className":1520,"ariaHidden":614},[613],[584,1522,1524,1527,1530,1533],{"className":1523},[618],[584,1525],{"className":1526,"style":925},[622],[584,1528,1079],{"className":1529},[627],[584,1531],{"className":1532,"style":932},[684],[584,1534,1536],{"className":1535},[627,936],[584,1537,1514],{"className":1538},[627]," breit, unten ",[584,1541,1543,1561],{"className":1542},[587],[584,1544,1546],{"className":1545},[591],[593,1547,1548],{"xmlns":595},[597,1549,1550,1558],{},[600,1551,1552,1554,1556],{},[903,1553,905],{},[907,1555,909],{},[907,1557,1514],{},[607,1559,1560],{"encoding":609},"4\\,\\text{m}",[584,1562,1564],{"className":1563,"ariaHidden":614},[613],[584,1565,1567,1570,1573,1576],{"className":1566},[618],[584,1568],{"className":1569,"style":925},[622],[584,1571,905],{"className":1572},[627],[584,1574],{"className":1575,"style":932},[684],[584,1577,1579],{"className":1578},[627,936],[584,1580,1514],{"className":1581},[627],", und ",[584,1584,1586,1604],{"className":1585},[587],[584,1587,1589],{"className":1588},[591],[593,1590,1591],{"xmlns":595},[597,1592,1593,1601],{},[600,1594,1595,1597,1599],{},[903,1596,955],{},[907,1598,909],{},[907,1600,1514],{},[607,1602,1603],{"encoding":609},"3\\,\\text{m}",[584,1605,1607],{"className":1606,"ariaHidden":614},[613],[584,1608,1610,1613,1616,1619],{"className":1609},[618],[584,1611],{"className":1612,"style":925},[622],[584,1614,955],{"className":1615},[627],[584,1617],{"className":1618,"style":932},[684],[584,1620,1622],{"className":1621},[627,936],[584,1623,1514],{"className":1624},[627]," tief. Er ist ",[584,1627,1629,1648],{"className":1628},[587],[584,1630,1632],{"className":1631},[591],[593,1633,1634],{"xmlns":595},[597,1635,1636,1645],{},[600,1637,1638,1641,1643],{},[903,1639,1640],{},"8",[907,1642,909],{},[907,1644,1514],{},[607,1646,1647],{"encoding":609},"8\\,\\text{m}",[584,1649,1651],{"className":1650,"ariaHidden":614},[613],[584,1652,1654,1657,1660,1663],{"className":1653},[618],[584,1655],{"className":1656,"style":925},[622],[584,1658,1640],{"className":1659},[627],[584,1661],{"className":1662,"style":932},[684],[584,1664,1666],{"className":1665},[627,936],[584,1667,1514],{"className":1668},[627]," lang. Der Querschnitt ist die Grundfläche, die Länge die Höhe des Prismas:",[584,1671,1673],{"className":1672},[1032],[584,1674,1676,1780],{"className":1675},[587],[584,1677,1679],{"className":1678},[591],[593,1680,1681],{"xmlns":595,"display":1041},[597,1682,1683,1777],{},[600,1684,1685,1687,1689,1695,1697,1701,1703,1705,1707,1710,1712,1714,1716,1719,1721,1723,1725,1727,1729,1732,1734,1740,1742,1744,1746,1748,1750,1756,1758,1760,1762,1764,1766,1769,1771],{},[603,1686,651],{},[653,1688,655],{},[1051,1690,1691,1693],{},[903,1692,1055],{},[903,1694,1058],{},[653,1696,661],{},[653,1698,1700],{"stretchy":1699},"false","(",[903,1702,1079],{},[907,1704,909],{},[907,1706,1514],{},[653,1708,1709],{},"+",[903,1711,905],{},[907,1713,909],{},[907,1715,1514],{},[653,1717,1718],{"stretchy":1699},")",[653,1720,661],{},[903,1722,955],{},[907,1724,909],{},[907,1726,1514],{},[653,1728,655],{},[903,1730,1731],{},"15",[907,1733,909],{},[1083,1735,1736,1738],{},[907,1737,1514],{},[903,1739,1058],{},[684,1741],{"width":1091},[603,1743,738],{},[653,1745,655],{},[903,1747,1731],{},[907,1749,909],{},[1083,1751,1752,1754],{},[907,1753,1514],{},[903,1755,1058],{},[653,1757,661],{},[903,1759,1640],{},[907,1761,909],{},[907,1763,1514],{},[653,1765,655],{},[903,1767,1768],{},"120",[907,1770,909],{},[1083,1772,1773,1775],{},[907,1774,1514],{},[903,1776,955],{},[607,1778,1779],{"encoding":609},"G = \\frac{1}{2} \\cdot (6\\,\\text{m} + 4\\,\\text{m}) \\cdot 3\\,\\text{m} = 15\\,\\text{m}^2\n\\qquad\nV = 15\\,\\text{m}^2 \\cdot 8\\,\\text{m} = 120\\,\\text{m}^3",[584,1781,1783,1801,1878,1909,1939,1966,2025,2078,2105],{"className":1782,"ariaHidden":614},[613],[584,1784,1786,1789,1792,1795,1798],{"className":1785},[618],[584,1787],{"className":1788,"style":677},[622],[584,1790,651],{"className":1791},[627,628],[584,1793],{"className":1794,"style":685},[684],[584,1796,655],{"className":1797},[689],[584,1799],{"className":1800,"style":685},[684],[584,1802,1804,1807,1869,1872,1875],{"className":1803},[618],[584,1805],{"className":1806,"style":1157},[622],[584,1808,1810,1813,1866],{"className":1809},[627],[584,1811],{"className":1812},[1164,1165],[584,1814,1816],{"className":1815},[1051],[584,1817,1819,1858],{"className":1818},[1172,1173],[584,1820,1822,1855],{"className":1821},[1177],[584,1823,1825,1836,1844],{"className":1824,"style":1182},[1181],[584,1826,1827,1830],{"style":1185},[584,1828],{"className":1829,"style":1190},[1189],[584,1831,1833],{"className":1832},[627],[584,1834,1058],{"className":1835},[627],[584,1837,1838,1841],{"style":1199},[584,1839],{"className":1840,"style":1190},[1189],[584,1842],{"className":1843,"style":1207},[1206],[584,1845,1846,1849],{"style":1210},[584,1847],{"className":1848,"style":1190},[1189],[584,1850,1852],{"className":1851},[627],[584,1853,1055],{"className":1854},[627],[584,1856,1224],{"className":1857},[1223],[584,1859,1861],{"className":1860},[1177],[584,1862,1864],{"className":1863,"style":1231},[1181],[584,1865],{},[584,1867],{"className":1868},[1237,1165],[584,1870],{"className":1871,"style":706},[684],[584,1873,661],{"className":1874},[710],[584,1876],{"className":1877,"style":706},[684],[584,1879,1881,1885,1888,1891,1894,1900,1903,1906],{"className":1880},[618],[584,1882],{"className":1883,"style":1884},[622],"height:1em;vertical-align:-0.25em;",[584,1886,1700],{"className":1887},[1164],[584,1889,1079],{"className":1890},[627],[584,1892],{"className":1893,"style":932},[684],[584,1895,1897],{"className":1896},[627,936],[584,1898,1514],{"className":1899},[627],[584,1901],{"className":1902,"style":706},[684],[584,1904,1709],{"className":1905},[710],[584,1907],{"className":1908,"style":706},[684],[584,1910,1912,1915,1918,1921,1927,1930,1933,1936],{"className":1911},[618],[584,1913],{"className":1914,"style":1884},[622],[584,1916,905],{"className":1917},[627],[584,1919],{"className":1920,"style":932},[684],[584,1922,1924],{"className":1923},[627,936],[584,1925,1514],{"className":1926},[627],[584,1928,1718],{"className":1929},[1237],[584,1931],{"className":1932,"style":706},[684],[584,1934,661],{"className":1935},[710],[584,1937],{"className":1938,"style":706},[684],[584,1940,1942,1945,1948,1951,1957,1960,1963],{"className":1941},[618],[584,1943],{"className":1944,"style":925},[622],[584,1946,955],{"className":1947},[627],[584,1949],{"className":1950,"style":932},[684],[584,1952,1954],{"className":1953},[627,936],[584,1955,1514],{"className":1956},[627],[584,1958],{"className":1959,"style":685},[684],[584,1961,655],{"className":1962},[689],[584,1964],{"className":1965,"style":685},[684],[584,1967,1969,1972,1975,1978,2010,2013,2016,2019,2022],{"className":1968},[618],[584,1970],{"className":1971,"style":1307},[622],[584,1973,1731],{"className":1974},[627],[584,1976],{"className":1977,"style":932},[684],[584,1979,1981,1987],{"className":1980},[627],[584,1982,1984],{"className":1983},[627,936],[584,1985,1514],{"className":1986},[627],[584,1988,1990],{"className":1989},[1326],[584,1991,1993],{"className":1992},[1172],[584,1994,1996],{"className":1995},[1177],[584,1997,1999],{"className":1998,"style":1307},[1181],[584,2000,2001,2004],{"style":1338},[584,2002],{"className":2003,"style":1342},[1189],[584,2005,2007],{"className":2006},[1346,1347,1348,1349],[584,2008,1058],{"className":2009},[627,1349],[584,2011],{"className":2012,"style":1356},[684],[584,2014,738],{"className":2015,"style":706},[627,628],[584,2017],{"className":2018,"style":685},[684],[584,2020,655],{"className":2021},[689],[584,2023],{"className":2024,"style":685},[684],[584,2026,2028,2031,2034,2037,2069,2072,2075],{"className":2027},[618],[584,2029],{"className":2030,"style":1307},[622],[584,2032,1731],{"className":2033},[627],[584,2035],{"className":2036,"style":932},[684],[584,2038,2040,2046],{"className":2039},[627],[584,2041,2043],{"className":2042},[627,936],[584,2044,1514],{"className":2045},[627],[584,2047,2049],{"className":2048},[1326],[584,2050,2052],{"className":2051},[1172],[584,2053,2055],{"className":2054},[1177],[584,2056,2058],{"className":2057,"style":1307},[1181],[584,2059,2060,2063],{"style":1338},[584,2061],{"className":2062,"style":1342},[1189],[584,2064,2066],{"className":2065},[1346,1347,1348,1349],[584,2067,1058],{"className":2068},[627,1349],[584,2070],{"className":2071,"style":706},[684],[584,2073,661],{"className":2074},[710],[584,2076],{"className":2077,"style":706},[684],[584,2079,2081,2084,2087,2090,2096,2099,2102],{"className":2080},[618],[584,2082],{"className":2083,"style":925},[622],[584,2085,1640],{"className":2086},[627],[584,2088],{"className":2089,"style":932},[684],[584,2091,2093],{"className":2092},[627,936],[584,2094,1514],{"className":2095},[627],[584,2097],{"className":2098,"style":685},[684],[584,2100,655],{"className":2101},[689],[584,2103],{"className":2104,"style":685},[684],[584,2106,2108,2111,2114,2117],{"className":2107},[618],[584,2109],{"className":2110,"style":1307},[622],[584,2112,1768],{"className":2113},[627],[584,2115],{"className":2116,"style":932},[684],[584,2118,2120,2126],{"className":2119},[627],[584,2121,2123],{"className":2122},[627,936],[584,2124,1514],{"className":2125},[627],[584,2127,2129],{"className":2128},[1326],[584,2130,2132],{"className":2131},[1172],[584,2133,2135],{"className":2134},[1177],[584,2136,2138],{"className":2137,"style":1307},[1181],[584,2139,2140,2143],{"style":1338},[584,2141],{"className":2142,"style":1342},[1189],[584,2144,2146],{"className":2145},[1346,1347,1348,1349],[584,2147,955],{"className":2148},[627,1349],[559,2150,2152],{"id":2151},"typische-fehler","Typische Fehler",[2154,2155,2156,2160,2267],"ul",{},[2157,2158,2159],"li",{},"Die Höhe des Grunddreiecks mit der Höhe des Prismas verwechseln. Es sind zwei verschiedene Strecken.",[2157,2161,2162,2163,2266],{},"Bei der Grundfläche des Dreiecks das ",[584,2164,2166,2184],{"className":2165},[587],[584,2167,2169],{"className":2168},[591],[593,2170,2171],{"xmlns":595},[597,2172,2173,2181],{},[600,2174,2175],{},[1051,2176,2177,2179],{},[903,2178,1055],{},[903,2180,1058],{},[607,2182,2183],{"encoding":609},"\\frac{1}{2}",[584,2185,2187],{"className":2186,"ariaHidden":614},[613],[584,2188,2190,2194],{"className":2189},[618],[584,2191],{"className":2192,"style":2193},[622],"height:1.1901em;vertical-align:-0.345em;",[584,2195,2197,2200,2263],{"className":2196},[627],[584,2198],{"className":2199},[1164,1165],[584,2201,2203],{"className":2202},[1051],[584,2204,2206,2254],{"className":2205},[1172,1173],[584,2207,2209,2251],{"className":2208},[1177],[584,2210,2213,2228,2236],{"className":2211,"style":2212},[1181],"height:0.8451em;",[584,2214,2216,2219],{"style":2215},"top:-2.655em;",[584,2217],{"className":2218,"style":1190},[1189],[584,2220,2222],{"className":2221},[1346,1347,1348,1349],[584,2223,2225],{"className":2224},[627,1349],[584,2226,1058],{"className":2227},[627,1349],[584,2229,2230,2233],{"style":1199},[584,2231],{"className":2232,"style":1190},[1189],[584,2234],{"className":2235,"style":1207},[1206],[584,2237,2239,2242],{"style":2238},"top:-3.394em;",[584,2240],{"className":2241,"style":1190},[1189],[584,2243,2245],{"className":2244},[1346,1347,1348,1349],[584,2246,2248],{"className":2247},[627,1349],[584,2249,1055],{"className":2250},[627,1349],[584,2252,1224],{"className":2253},[1223],[584,2255,2257],{"className":2256},[1177],[584,2258,2261],{"className":2259,"style":2260},[1181],"height:0.345em;",[584,2262],{},[584,2264],{"className":2265},[1237,1165]," vergessen.",[2157,2268,2269],{},"Bei einem liegenden Prisma die falsche Fläche als Grundfläche nehmen. Die Grundfläche ist die Querschnittsfläche, die sich entlang der Höhe nicht ändert.",{"title":2271,"searchDepth":2272,"depth":2272,"links":2273},"",2,[2274,2275,2276],{"id":561,"depth":2272,"text":562},{"id":885,"depth":2272,"text":886},{"id":2151,"depth":2272,"text":2152},[2278,2280,2282,2284],{"lhs":2279,"rhs":1079},"1\u002F2 * 4 * 3",{"lhs":2281,"rhs":1118},"6 * 10",{"lhs":2283,"rhs":1731},"1\u002F2 * (6 + 4) * 3",{"lhs":2285,"rhs":1768},"15 * 8",null,"md",{"caption":2289,"x":2290,"y":2293,"items":2295},"Gerades Dreiecksprisma mit der Grundfläche G und der Höhe h",[2291,2292],-0.7,3.6,[2294,2292],-0.6,[2296,2308,2312,2315,2318,2322,2326,2329,2332,2335,2338,2343],{"type":2297,"points":2298,"fill":2306,"style":2307},"polygon",[2299,2301,2303],[2300,2300],0,[2302,2300],3,[2304,2305],2.5,1.05,true,"dashed",{"type":2309,"from":2310,"to":2311},"segment",[2300,2300],[2302,2300],{"type":2309,"from":2313,"to":2314,"style":2307},[2302,2300],[2304,2305],{"type":2309,"from":2316,"to":2317,"style":2307},[2304,2305],[2300,2300],{"type":2309,"from":2319,"to":2321},[2300,2320],2.2,[2302,2320],{"type":2309,"from":2323,"to":2324},[2302,2320],[2304,2325],3.25,{"type":2309,"from":2327,"to":2328},[2304,2325],[2300,2320],{"type":2309,"from":2330,"to":2331},[2300,2300],[2300,2320],{"type":2309,"from":2333,"to":2334},[2302,2300],[2302,2320],{"type":2309,"from":2336,"to":2337,"style":2307},[2304,2305],[2304,2325],{"type":2339,"at":2340,"text":605},"label",[2341,2342],-0.3,1.1,{"type":2339,"at":2344,"text":651},[2345,2346],1.65,0.38,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 206.4 201.6\" width=\"206.4\" height=\"201.6\" role=\"img\" aria-label=\"Gerades Dreiecksprisma mit der Grundfläche G und der Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-prism-volume-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-prism-volume-clip\">\u003Crect x=\"0\" y=\"0\" width=\"206.4\" height=\"201.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"33.6,172.8 177.6,172.8 153.6,122.4\" class=\"fig-dashed fig-fill\"\u002F>\u003Cline x1=\"33.6\" y1=\"172.8\" x2=\"177.6\" y2=\"172.8\" class=\"fig-main\"\u002F>\u003Cline x1=\"177.6\" y1=\"172.8\" x2=\"153.6\" y2=\"122.4\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"153.6\" y1=\"122.4\" x2=\"33.6\" y2=\"172.8\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"33.6\" y1=\"67.2\" x2=\"177.6\" y2=\"67.2\" class=\"fig-main\"\u002F>\u003Cline x1=\"177.6\" y1=\"67.2\" x2=\"153.6\" y2=\"16.8\" class=\"fig-main\"\u002F>\u003Cline x1=\"153.6\" y1=\"16.8\" x2=\"33.6\" y2=\"67.2\" class=\"fig-main\"\u002F>\u003Cline x1=\"33.6\" y1=\"172.8\" x2=\"33.6\" y2=\"67.2\" class=\"fig-main\"\u002F>\u003Cline x1=\"177.6\" y1=\"172.8\" x2=\"177.6\" y2=\"67.2\" class=\"fig-main\"\u002F>\u003Cline x1=\"153.6\" y1=\"122.4\" x2=\"153.6\" y2=\"16.8\" class=\"fig-dashed\"\u002F>\u003Ctext x=\"19.2\" y=\"120\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003Ctext x=\"112.8\" y=\"154.56\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">G\u003C\u002Ftext>\u003C\u002Fsvg>","prism-volume","V = G \\cdot h","\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>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = G \\cdot h\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\" style=\"margin-right:0.2222em;\">V\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-prisma",[],[2356,2357,2358,2359],"cuboid-volume","cylinder-volume","pyramid-volume","triangle-area",{"title":548,"description":2271},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-prisma","Das Volumen eines Prismas ist Grundfläche mal Höhe.",[2364,2365,2366,2367],"volumen","prisma","grundfläche","körper",[2369,2372,2375],{"symbol":738,"meaning":2370,"symbolHtml":2371},"Volumen des Prismas","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V\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\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":651,"meaning":2373,"symbolHtml":2374},"Flächeninhalt der Grundfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>G\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">G\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\">G\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":605,"meaning":2376,"symbolHtml":2377},"Höhe des Prismas, der senkrechte Abstand zwischen Grund- und Deckfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h\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\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","2h938CwH2qJA8Hi0GZWCC6BoXX_WyWMQshV2bzzVk08",[2380,2383,2386,2389],{"stem":2381,"title":2382,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-dreieck","Flächeninhalt eines Dreiecks",{"stem":2384,"title":2385,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-pyramide","Volumen einer Pyramide",{"stem":2387,"title":2388,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-quader","Volumen eines Quaders",{"stem":2390,"title":2391,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-zylinder","Volumen eines Zylinders",1793824270835]