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hoch:",[582,917,920],{"className":918},[919],"katex-display",[582,921,923,1022],{"className":922},[585],[582,924,926],{"className":925},[589],[591,927,929],{"xmlns":593,"display":928},"block",[595,930,931,1019],{},[598,932,933,936,939,941,943,947,950,952,959,962,965,967,973,975,978,980,986,989,991,993,995,998,1000,1006,1008,1011,1013],{},[601,934,935],{},"O",[605,937,938],{},"=",[790,940,886],{},[605,942,607],{},[605,944,946],{"stretchy":945},"false","(",[790,948,949],{},"15",[794,951,796],{},[953,954,955,957],"msup",{},[794,956,799],{},[790,958,886],{},[605,960,961],{},"+",[790,963,964],{},"10",[794,966,796],{},[953,968,969,971],{},[794,970,799],{},[790,972,886],{},[605,974,961],{},[790,976,977],{},"6",[794,979,796],{},[953,981,982,984],{},[794,983,799],{},[790,985,886],{},[605,987,988],{"stretchy":945},")",[605,990,938],{},[790,992,886],{},[605,994,607],{},[790,996,997],{},"31",[794,999,796],{},[953,1001,1002,1004],{},[794,1003,799],{},[790,1005,886],{},[605,1007,938],{},[790,1009,1010],{},"62",[794,1012,796],{},[953,1014,1015,1017],{},[794,1016,799],{},[790,1018,886],{},[612,1020,1021],{"encoding":614},"O = 2 \\cdot (15\\,\\text{cm}^2 + 10\\,\\text{cm}^2 + 6\\,\\text{cm}^2) = 2 \\cdot 31\\,\\text{cm}^2 = 62\\,\\text{cm}^2",[582,1023,1025,1047,1065,1135,1189,1246,1264,1317],{"className":1024,"ariaHidden":620},[619],[582,1026,1028,1032,1036,1040,1044],{"className":1027},[624],[582,1029],{"className":1030,"style":1031},[628],"height:0.6833em;",[582,1033,935],{"className":1034,"style":1035},[633,634],"margin-right:0.0278em;",[582,1037],{"className":1038,"style":1039},[638],"margin-right:0.2778em;",[582,1041,938],{"className":1042},[1043],"mrel",[582,1045],{"className":1046,"style":1039},[638],[582,1048,1050,1053,1056,1059,1062],{"className":1049},[624],[582,1051],{"className":1052,"style":812},[628],[582,1054,886],{"className":1055},[633],[582,1057],{"className":1058,"style":639},[638],[582,1060,607],{"className":1061},[643],[582,1063],{"className":1064,"style":639},[638],[582,1066,1068,1072,1076,1079,1082,1126,1129,1132],{"className":1067},[624],[582,1069],{"className":1070,"style":1071},[628],"height:1.1141em;vertical-align:-0.25em;",[582,1073,946],{"className":1074},[1075],"mopen",[582,1077,949],{"className":1078},[633],[582,1080],{"className":1081,"style":819},[638],[582,1083,1085,1091],{"className":1084},[633],[582,1086,1088],{"className":1087},[633,823],[582,1089,799],{"className":1090},[633],[582,1092,1095],{"className":1093},[1094],"msupsub",[582,1096,1099],{"className":1097},[1098],"vlist-t",[582,1100,1103],{"className":1101},[1102],"vlist-r",[582,1104,1108],{"className":1105,"style":1107},[1106],"vlist","height:0.8641em;",[582,1109,1111,1116],{"style":1110},"top:-3.113em;margin-right:0.05em;",[582,1112],{"className":1113,"style":1115},[1114],"pstrut","height:2.7em;",[582,1117,1123],{"className":1118},[1119,1120,1121,1122],"sizing","reset-size6","size3","mtight",[582,1124,886],{"className":1125},[633,1122],[582,1127],{"className":1128,"style":639},[638],[582,1130,961],{"className":1131},[643],[582,1133],{"className":1134,"style":639},[638],[582,1136,1138,1142,1145,1148,1180,1183,1186],{"className":1137},[624],[582,1139],{"className":1140,"style":1141},[628],"height:0.9474em;vertical-align:-0.0833em;",[582,1143,964],{"className":1144},[633],[582,1146],{"className":1147,"style":819},[638],[582,1149,1151,1157],{"className":1150},[633],[582,1152,1154],{"className":1153},[633,823],[582,1155,799],{"className":1156},[633],[582,1158,1160],{"className":1159},[1094],[582,1161,1163],{"className":1162},[1098],[582,1164,1166],{"className":1165},[1102],[582,1167,1169],{"className":1168,"style":1107},[1106],[582,1170,1171,1174],{"style":1110},[582,1172],{"className":1173,"style":1115},[1114],[582,1175,1177],{"className":1176},[1119,1120,1121,1122],[582,1178,886],{"className":1179},[633,1122],[582,1181],{"className":1182,"style":639},[638],[582,1184,961],{"className":1185},[643],[582,1187],{"className":1188,"style":639},[638],[582,1190,1192,1195,1198,1201,1233,1237,1240,1243],{"className":1191},[624],[582,1193],{"className":1194,"style":1071},[628],[582,1196,977],{"className":1197},[633],[582,1199],{"className":1200,"style":819},[638],[582,1202,1204,1210],{"className":1203},[633],[582,1205,1207],{"className":1206},[633,823],[582,1208,799],{"className":1209},[633],[582,1211,1213],{"className":1212},[1094],[582,1214,1216],{"className":1215},[1098],[582,1217,1219],{"className":1218},[1102],[582,1220,1222],{"className":1221,"style":1107},[1106],[582,1223,1224,1227],{"style":1110},[582,1225],{"className":1226,"style":1115},[1114],[582,1228,1230],{"className":1229},[1119,1120,1121,1122],[582,1231,886],{"className":1232},[633,1122],[582,1234,988],{"className":1235},[1236],"mclose",[582,1238],{"className":1239,"style":1039},[638],[582,1241,938],{"className":1242},[1043],[582,1244],{"className":1245,"style":1039},[638],[582,1247,1249,1252,1255,1258,1261],{"className":1248},[624],[582,1250],{"className":1251,"style":812},[628],[582,1253,886],{"className":1254},[633],[582,1256],{"className":1257,"style":639},[638],[582,1259,607],{"className":1260},[643],[582,1262],{"className":1263,"style":639},[638],[582,1265,1267,1270,1273,1276,1308,1311,1314],{"className":1266},[624],[582,1268],{"className":1269,"style":1107},[628],[582,1271,997],{"className":1272},[633],[582,1274],{"className":1275,"style":819},[638],[582,1277,1279,1285],{"className":1278},[633],[582,1280,1282],{"className":1281},[633,823],[582,1283,799],{"className":1284},[633],[582,1286,1288],{"className":1287},[1094],[582,1289,1291],{"className":1290},[1098],[582,1292,1294],{"className":1293},[1102],[582,1295,1297],{"className":1296,"style":1107},[1106],[582,1298,1299,1302],{"style":1110},[582,1300],{"className":1301,"style":1115},[1114],[582,1303,1305],{"className":1304},[1119,1120,1121,1122],[582,1306,886],{"className":1307},[633,1122],[582,1309],{"className":1310,"style":1039},[638],[582,1312,938],{"className":1313},[1043],[582,1315],{"className":1316,"style":1039},[638],[582,1318,1320,1323,1326,1329],{"className":1319},[624],[582,1321],{"className":1322,"style":1107},[628],[582,1324,1010],{"className":1325},[633],[582,1327],{"className":1328,"style":819},[638],[582,1330,1332,1338],{"className":1331},[633],[582,1333,1335],{"className":1334},[633,823],[582,1336,799],{"className":1337},[633],[582,1339,1341],{"className":1340},[1094],[582,1342,1344],{"className":1343},[1098],[582,1345,1347],{"className":1346},[1102],[582,1348,1350],{"className":1349,"style":1107},[1106],[582,1351,1352,1355],{"style":1110},[582,1353],{"className":1354,"style":1115},[1114],[582,1356,1358],{"className":1357},[1119,1120,1121,1122],[582,1359,886],{"className":1360},[633,1122],[563,1362,1363,1364,827,1407,871,1450,1492],{},"Ein Karton ist ",[582,1365,1367,1386],{"className":1366},[585],[582,1368,1370],{"className":1369},[589],[591,1371,1372],{"xmlns":593},[595,1373,1374,1383],{},[598,1375,1376,1379,1381],{},[790,1377,1378],{},"30",[794,1380,796],{},[794,1382,799],{},[612,1384,1385],{"encoding":614},"30\\,\\text{cm}",[582,1387,1389],{"className":1388,"ariaHidden":620},[619],[582,1390,1392,1395,1398,1401],{"className":1391},[624],[582,1393],{"className":1394,"style":812},[628],[582,1396,1378],{"className":1397},[633],[582,1399],{"className":1400,"style":819},[638],[582,1402,1404],{"className":1403},[633,823],[582,1405,799],{"className":1406},[633],[582,1408,1410,1429],{"className":1409},[585],[582,1411,1413],{"className":1412},[589],[591,1414,1415],{"xmlns":593},[595,1416,1417,1426],{},[598,1418,1419,1422,1424],{},[790,1420,1421],{},"20",[794,1423,796],{},[794,1425,799],{},[612,1427,1428],{"encoding":614},"20\\,\\text{cm}",[582,1430,1432],{"className":1431,"ariaHidden":620},[619],[582,1433,1435,1438,1441,1444],{"className":1434},[624],[582,1436],{"className":1437,"style":812},[628],[582,1439,1421],{"className":1440},[633],[582,1442],{"className":1443,"style":819},[638],[582,1445,1447],{"className":1446},[633,823],[582,1448,799],{"className":1449},[633],[582,1451,1453,1471],{"className":1452},[585],[582,1454,1456],{"className":1455},[589],[591,1457,1458],{"xmlns":593},[595,1459,1460,1468],{},[598,1461,1462,1464,1466],{},[790,1463,964],{},[794,1465,796],{},[794,1467,799],{},[612,1469,1470],{"encoding":614},"10\\,\\text{cm}",[582,1472,1474],{"className":1473,"ariaHidden":620},[619],[582,1475,1477,1480,1483,1486],{"className":1476},[624],[582,1478],{"className":1479,"style":812},[628],[582,1481,964],{"className":1482},[633],[582,1484],{"className":1485,"style":819},[638],[582,1487,1489],{"className":1488},[633,823],[582,1490,799],{"className":1491},[633]," hoch. Ohne Überlappung braucht man so viel Pappe:",[582,1494,1496],{"className":1495},[919],[582,1497,1499,1573],{"className":1498},[585],[582,1500,1502],{"className":1501},[589],[591,1503,1504],{"xmlns":593,"display":928},[595,1505,1506,1570],{},[598,1507,1508,1510,1512,1514,1516,1518,1521,1523,1529,1531,1534,1536,1542,1544,1547,1549,1555,1557,1559,1562,1564],{},[601,1509,935],{},[605,1511,938],{},[790,1513,886],{},[605,1515,607],{},[605,1517,946],{"stretchy":945},[790,1519,1520],{},"600",[794,1522,796],{},[953,1524,1525,1527],{},[794,1526,799],{},[790,1528,886],{},[605,1530,961],{},[790,1532,1533],{},"300",[794,1535,796],{},[953,1537,1538,1540],{},[794,1539,799],{},[790,1541,886],{},[605,1543,961],{},[790,1545,1546],{},"200",[794,1548,796],{},[953,1550,1551,1553],{},[794,1552,799],{},[790,1554,886],{},[605,1556,988],{"stretchy":945},[605,1558,938],{},[790,1560,1561],{},"2200",[794,1563,796],{},[953,1565,1566,1568],{},[794,1567,799],{},[790,1569,886],{},[612,1571,1572],{"encoding":614},"O = 2 \\cdot (600\\,\\text{cm}^2 + 300\\,\\text{cm}^2 + 200\\,\\text{cm}^2) = 2200\\,\\text{cm}^2",[582,1574,1576,1594,1612,1668,1721,1777],{"className":1575,"ariaHidden":620},[619],[582,1577,1579,1582,1585,1588,1591],{"className":1578},[624],[582,1580],{"className":1581,"style":1031},[628],[582,1583,935],{"className":1584,"style":1035},[633,634],[582,1586],{"className":1587,"style":1039},[638],[582,1589,938],{"className":1590},[1043],[582,1592],{"className":1593,"style":1039},[638],[582,1595,1597,1600,1603,1606,1609],{"className":1596},[624],[582,1598],{"className":1599,"style":812},[628],[582,1601,886],{"className":1602},[633],[582,1604],{"className":1605,"style":639},[638],[582,1607,607],{"className":1608},[643],[582,1610],{"className":1611,"style":639},[638],[582,1613,1615,1618,1621,1624,1627,1659,1662,1665],{"className":1614},[624],[582,1616],{"className":1617,"style":1071},[628],[582,1619,946],{"className":1620},[1075],[582,1622,1520],{"className":1623},[633],[582,1625],{"className":1626,"style":819},[638],[582,1628,1630,1636],{"className":1629},[633],[582,1631,1633],{"className":1632},[633,823],[582,1634,799],{"className":1635},[633],[582,1637,1639],{"className":1638},[1094],[582,1640,1642],{"className":1641},[1098],[582,1643,1645],{"className":1644},[1102],[582,1646,1648],{"className":1647,"style":1107},[1106],[582,1649,1650,1653],{"style":1110},[582,1651],{"className":1652,"style":1115},[1114],[582,1654,1656],{"className":1655},[1119,1120,1121,1122],[582,1657,886],{"className":1658},[633,1122],[582,1660],{"className":1661,"style":639},[638],[582,1663,961],{"className":1664},[643],[582,1666],{"className":1667,"style":639},[638],[582,1669,1671,1674,1677,1680,1712,1715,1718],{"className":1670},[624],[582,1672],{"className":1673,"style":1141},[628],[582,1675,1533],{"className":1676},[633],[582,1678],{"className":1679,"style":819},[638],[582,1681,1683,1689],{"className":1682},[633],[582,1684,1686],{"className":1685},[633,823],[582,1687,799],{"className":1688},[633],[582,1690,1692],{"className":1691},[1094],[582,1693,1695],{"className":1694},[1098],[582,1696,1698],{"className":1697},[1102],[582,1699,1701],{"className":1700,"style":1107},[1106],[582,1702,1703,1706],{"style":1110},[582,1704],{"className":1705,"style":1115},[1114],[582,1707,1709],{"className":1708},[1119,1120,1121,1122],[582,1710,886],{"className":1711},[633,1122],[582,1713],{"className":1714,"style":639},[638],[582,1716,961],{"className":1717},[643],[582,1719],{"className":1720,"style":639},[638],[582,1722,1724,1727,1730,1733,1765,1768,1771,1774],{"className":1723},[624],[582,1725],{"className":1726,"style":1071},[628],[582,1728,1546],{"className":1729},[633],[582,1731],{"className":1732,"style":819},[638],[582,1734,1736,1742],{"className":1735},[633],[582,1737,1739],{"className":1738},[633,823],[582,1740,799],{"className":1741},[633],[582,1743,1745],{"className":1744},[1094],[582,1746,1748],{"className":1747},[1098],[582,1749,1751],{"className":1750},[1102],[582,1752,1754],{"className":1753,"style":1107},[1106],[582,1755,1756,1759],{"style":1110},[582,1757],{"className":1758,"style":1115},[1114],[582,1760,1762],{"className":1761},[1119,1120,1121,1122],[582,1763,886],{"className":1764},[633,1122],[582,1766,988],{"className":1767},[1236],[582,1769],{"className":1770,"style":1039},[638],[582,1772,938],{"className":1773},[1043],[582,1775],{"className":1776,"style":1039},[638],[582,1778,1780,1783,1786,1789],{"className":1779},[624],[582,1781],{"className":1782,"style":1107},[628],[582,1784,1561],{"className":1785},[633],[582,1787],{"className":1788,"style":819},[638],[582,1790,1792,1798],{"className":1791},[633],[582,1793,1795],{"className":1794},[633,823],[582,1796,799],{"className":1797},[633],[582,1799,1801],{"className":1800},[1094],[582,1802,1804],{"className":1803},[1098],[582,1805,1807],{"className":1806},[1102],[582,1808,1810],{"className":1809,"style":1107},[1106],[582,1811,1812,1815],{"style":1110},[582,1813],{"className":1814,"style":1115},[1114],[582,1816,1818],{"className":1817},[1119,1120,1121,1122],[582,1819,886],{"className":1820},[633,1122],[558,1822,1824],{"id":1823},"typische-fehler","Typische Fehler",[575,1826,1827,1830,1961],{},[578,1828,1829],{},"Das „mal 2\" vergessen. Dann hat man nur drei der sechs Seiten.",[578,1831,1832,1833,1897,1898,1960],{},"Volumen und Oberfläche verwechseln: Die Oberfläche hat die Einheit ",[582,1834,1836,1854],{"className":1835},[585],[582,1837,1839],{"className":1838},[589],[591,1840,1841],{"xmlns":593},[595,1842,1843,1851],{},[598,1844,1845],{},[953,1846,1847,1849],{},[794,1848,799],{},[790,1850,886],{},[612,1852,1853],{"encoding":614},"\\text{cm}^2",[582,1855,1857],{"className":1856,"ariaHidden":620},[619],[582,1858,1860,1864],{"className":1859},[624],[582,1861],{"className":1862,"style":1863},[628],"height:0.8141em;",[582,1865,1867,1873],{"className":1866},[633],[582,1868,1870],{"className":1869},[633,823],[582,1871,799],{"className":1872},[633],[582,1874,1876],{"className":1875},[1094],[582,1877,1879],{"className":1878},[1098],[582,1880,1882],{"className":1881},[1102],[582,1883,1885],{"className":1884,"style":1863},[1106],[582,1886,1888,1891],{"style":1887},"top:-3.063em;margin-right:0.05em;",[582,1889],{"className":1890,"style":1115},[1114],[582,1892,1894],{"className":1893},[1119,1120,1121,1122],[582,1895,886],{"className":1896},[633,1122],", das Volumen ",[582,1899,1901,1919],{"className":1900},[585],[582,1902,1904],{"className":1903},[589],[591,1905,1906],{"xmlns":593},[595,1907,1908,1916],{},[598,1909,1910],{},[953,1911,1912,1914],{},[794,1913,799],{},[790,1915,842],{},[612,1917,1918],{"encoding":614},"\\text{cm}^3",[582,1920,1922],{"className":1921,"ariaHidden":620},[619],[582,1923,1925,1928],{"className":1924},[624],[582,1926],{"className":1927,"style":1863},[628],[582,1929,1931,1937],{"className":1930},[633],[582,1932,1934],{"className":1933},[633,823],[582,1935,799],{"className":1936},[633],[582,1938,1940],{"className":1939},[1094],[582,1941,1943],{"className":1942},[1098],[582,1944,1946],{"className":1945},[1102],[582,1947,1949],{"className":1948,"style":1863},[1106],[582,1950,1951,1954],{"style":1887},[582,1952],{"className":1953,"style":1115},[1114],[582,1955,1957],{"className":1956},[1119,1120,1121,1122],[582,1958,842],{"className":1959},[633,1122],".",[578,1962,1963,1964,1960],{},"Bei einem oben offenen Körper (z.B. Kiste ohne Deckel) trotzdem sechs Flächen zählen. Dann fehlt einmal ",[582,1965,1967,1984],{"className":1966},[585],[582,1968,1970],{"className":1969},[589],[591,1971,1972],{"xmlns":593},[595,1973,1974,1982],{},[598,1975,1976,1978,1980],{},[601,1977,603],{},[605,1979,607],{},[601,1981,610],{},[612,1983,615],{"encoding":614},[582,1985,1987,2005],{"className":1986,"ariaHidden":620},[619],[582,1988,1990,1993,1996,1999,2002],{"className":1989},[624],[582,1991],{"className":1992,"style":629},[628],[582,1994,603],{"className":1995},[633,634],[582,1997],{"className":1998,"style":639},[638],[582,2000,607],{"className":2001},[643],[582,2003],{"className":2004,"style":639},[638],[582,2006,2008,2011],{"className":2007},[624],[582,2009],{"className":2010,"style":653},[628],[582,2012,610],{"className":2013},[633,634],{"title":2015,"searchDepth":2016,"depth":2016,"links":2017},"",2,[2018,2019,2020],{"id":560,"depth":2016,"text":561},{"id":772,"depth":2016,"text":773},{"id":1823,"depth":2016,"text":1824},[2022,2025,2027],{"lhs":2023,"rhs":2024},"2 * (a*b + a*c + b*c)","2*a*b + 2*a*c + 2*b*c",{"lhs":2026,"rhs":1010},"2 * (5*3 + 5*2 + 3*2)",{"lhs":2028,"rhs":1561},"2 * (30*20 + 30*10 + 20*10)",null,"md",{"caption":2032,"x":2033,"y":2036,"items":2039},"Quader mit Länge a, Breite b und Höhe c; die sichtbaren Seitenflächen sind 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