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werden:",[572,1201,1203],{"className":1202},[844],[572,1204,1206,1270],{"className":1205},[575],[572,1207,1209],{"className":1208},[579],[581,1210,1211],{"xmlns":583,"display":853},[585,1212,1213,1267],{},[588,1214,1215,1217,1219,1221,1223,1225,1227,1229,1231,1237,1239,1241,1243,1246,1248,1254,1256,1259,1261],{},[594,1216,860],{},[679,1218,863],{},[598,1220,677],{},[679,1222,681],{},[679,1224,871],{"stretchy":870},[598,1226,1157],{},[808,1228,810],{},[808,1230,813],{},[591,1232,1233,1235],{},[679,1234,882],{"stretchy":870},[598,1236,600],{},[679,1238,863],{},[598,1240,677],{},[679,1242,681],{},[598,1244,1245],{},"6,25",[808,1247,810],{},[591,1249,1250,1252],{},[808,1251,813],{},[598,1253,600],{},[679,1255,863],{},[598,1257,1258],{},"37,5",[808,1260,810],{},[591,1262,1263,1265],{},[808,1264,813],{},[598,1266,600],{},[602,1268,1269],{"encoding":604},"O = 6 \\cdot (2{,}5\\,\\text{cm})^2 = 6 \\cdot 6{,}25\\,\\text{cm}^2 = 37{,}5\\,\\text{cm}^2",[572,1271,1273,1291,1309,1377,1395,1459],{"className":1272,"ariaHidden":610},[609],[572,1274,1276,1279,1282,1285,1288],{"className":1275},[614],[572,1277],{"className":1278,"style":927},[618],[572,1280,860],{"className":1281,"style":931},[623,627],[572,1283],{"className":1284,"style":935},[707],[572,1286,863],{"className":1287},[939],[572,1289],{"className":1290,"style":935},[707],[572,1292,1294,1297,1300,1303,1306],{"className":1293},[614],[572,1295],{"className":1296,"style":700},[618],[572,1298,677],{"className":1299},[623],[572,1301],{"className":1302,"style":708},[707],[572,1304,681],{"className":1305},[712],[572,1307],{"className":1308,"style":708},[707],[572,1310,1312,1315,1318,1321,1327,1330,1333,1339,1368,1371,1374],{"className":1311},[614],[572,1313],{"className":1314,"style":967},[618],[572,1316,871],{"className":1317},[971],[572,1319,600],{"className":1320},[623],[572,1322,1324],{"className":1323},[623],[572,1325,1185],{"className":1326},[1184],[572,1328,1189],{"className":1329},[623],[572,1331],{"className":1332,"style":832},[707],[572,1334,1336],{"className":1335},[623,836],[572,1337,813],{"className":1338},[623],[572,1340,1342,1345],{"className":1341},[987],[572,1343,882],{"className":1344},[987],[572,1346,1348],{"className":1347},[631],[572,1349,1351],{"className":1350},[635],[572,1352,1354],{"className":1353},[639],[572,1355,1357],{"className":1356,"style":1003},[643],[572,1358,1359,1362],{"style":1006},[572,1360],{"className":1361,"style":651},[650],[572,1363,1365],{"className":1364},[655,656,657,658],[572,1366,600],{"className":1367},[623,658],[572,1369],{"className":1370,"style":935},[707],[572,1372,863],{"className":1373},[939],[572,1375],{"className":1376,"style":935},[707],[572,1378,1380,1383,1386,1389,1392],{"className":1379},[614],[572,1381],{"className":1382,"style":700},[618],[572,1384,677],{"className":1385},[623],[572,1387],{"className":1388,"style":708},[707],[572,1390,681],{"className":1391},[712],[572,1393],{"className":1394,"style":708},[707],[572,1396,1398,1402,1405,1411,1415,1418,1450,1453,1456],{"className":1397},[614],[572,1399],{"className":1400,"style":1401},[618],"height:1.0585em;vertical-align:-0.1944em;",[572,1403,677],{"className":1404},[623],[572,1406,1408],{"className":1407},[623],[572,1409,1185],{"className":1410},[1184],[572,1412,1414],{"className":1413},[623],"25",[572,1416],{"className":1417,"style":832},[707],[572,1419,1421,1427],{"className":1420},[623],[572,1422,1424],{"className":1423},[623,836],[572,1425,813],{"className":1426},[623],[572,1428,1430],{"className":1429},[631],[572,1431,1433],{"className":1432},[635],[572,1434,1436],{"className":1435},[639],[572,1437,1439],{"className":1438,"style":1003},[643],[572,1440,1441,1444],{"style":1006},[572,1442],{"className":1443,"style":651},[650],[572,1445,1447],{"className":1446},[655,656,657,658],[572,1448,600],{"className":1449},[623,658],[572,1451],{"className":1452,"style":935},[707],[572,1454,863],{"className":1455},[939],[572,1457],{"className":1458,"style":935},[707],[572,1460,1462,1465,1469,1475,1478,1481],{"className":1461},[614],[572,1463],{"className":1464,"style":1401},[618],[572,1466,1468],{"className":1467},[623],"37",[572,1470,1472],{"className":1471},[623],[572,1473,1185],{"className":1474},[1184],[572,1476,1189],{"className":1477},[623],[572,1479],{"className":1480,"style":832},[707],[572,1482,1484,1490],{"className":1483},[623],[572,1485,1487],{"className":1486},[623,836],[572,1488,813],{"className":1489},[623],[572,1491,1493],{"className":1492},[631],[572,1494,1496],{"className":1495},[635],[572,1497,1499],{"className":1498},[639],[572,1500,1502],{"className":1501,"style":1003},[643],[572,1503,1504,1507],{"style":1006},[572,1505],{"className":1506,"style":651},[650],[572,1508,1510],{"className":1509},[655,656,657,658],[572,1511,600],{"className":1512},[623,658],[558,1514,1516],{"id":1515},"typische-fehler","Typische Fehler",[1518,1519,1520,1796],"ul",{},[1521,1522,1523,1524,1575,1576,1692,1693,751],"li",{},"Erst ",[572,1525,1527,1545],{"className":1526},[575],[572,1528,1530],{"className":1529},[579],[581,1531,1532],{"xmlns":583},[585,1533,1534,1542],{},[588,1535,1536,1538,1540],{},[598,1537,677],{},[679,1539,681],{},[594,1541,596],{},[602,1543,1544],{"encoding":604},"6 \\cdot a",[572,1546,1548,1566],{"className":1547,"ariaHidden":610},[609],[572,1549,1551,1554,1557,1560,1563],{"className":1550},[614],[572,1552],{"className":1553,"style":700},[618],[572,1555,677],{"className":1556},[623],[572,1558],{"className":1559,"style":708},[707],[572,1561,681],{"className":1562},[712],[572,1564],{"className":1565,"style":708},[707],[572,1567,1569,1572],{"className":1568},[614],[572,1570],{"className":1571,"style":780},[618],[572,1573,596],{"className":1574},[623,627]," rechnen und dann quadrieren: ",[572,1577,1579,1610],{"className":1578},[575],[572,1580,1582],{"className":1581},[579],[581,1583,1584],{"xmlns":583},[585,1585,1586,1607],{},[588,1587,1588,1590,1592,1594,1596,1602,1604],{},[679,1589,871],{"stretchy":870},[598,1591,677],{},[679,1593,681],{},[598,1595,806],{},[591,1597,1598,1600],{},[679,1599,882],{"stretchy":870},[598,1601,600],{},[679,1603,863],{},[598,1605,1606],{},"324",[602,1608,1609],{"encoding":604},"(6 \\cdot 3)^2 = 324",[572,1611,1613,1635,1683],{"className":1612,"ariaHidden":610},[609],[572,1614,1616,1620,1623,1626,1629,1632],{"className":1615},[614],[572,1617],{"className":1618,"style":1619},[618],"height:1em;vertical-align:-0.25em;",[572,1621,871],{"className":1622},[971],[572,1624,677],{"className":1625},[623],[572,1627],{"className":1628,"style":708},[707],[572,1630,681],{"className":1631},[712],[572,1633],{"className":1634,"style":708},[707],[572,1636,1638,1642,1645,1674,1677,1680],{"className":1637},[614],[572,1639],{"className":1640,"style":1641},[618],"height:1.0641em;vertical-align:-0.25em;",[572,1643,806],{"className":1644},[623],[572,1646,1648,1651],{"className":1647},[987],[572,1649,882],{"className":1650},[987],[572,1652,1654],{"className":1653},[631],[572,1655,1657],{"className":1656},[635],[572,1658,1660],{"className":1659},[639],[572,1661,1663],{"className":1662,"style":619},[643],[572,1664,1665,1668],{"style":646},[572,1666],{"className":1667,"style":651},[650],[572,1669,1671],{"className":1670},[655,656,657,658],[572,1672,600],{"className":1673},[623,658],[572,1675],{"className":1676,"style":935},[707],[572,1678,863],{"className":1679},[939],[572,1681],{"className":1682,"style":935},[707],[572,1684,1686,1689],{"className":1685},[614],[572,1687],{"className":1688,"style":700},[618],[572,1690,1606],{"className":1691},[623]," ist falsch, richtig ist ",[572,1694,1696,1722],{"className":1695},[575],[572,1697,1699],{"className":1698},[579],[581,1700,1701],{"xmlns":583},[585,1702,1703,1719],{},[588,1704,1705,1707,1709,1715,1717],{},[598,1706,677],{},[679,1708,681],{},[591,1710,1711,1713],{},[598,1712,806],{},[598,1714,600],{},[679,1716,863],{},[598,1718,906],{},[602,1720,1721],{"encoding":604},"6 \\cdot 3^2 = 54",[572,1723,1725,1743,1787],{"className":1724,"ariaHidden":610},[609],[572,1726,1728,1731,1734,1737,1740],{"className":1727},[614],[572,1729],{"className":1730,"style":700},[618],[572,1732,677],{"className":1733},[623],[572,1735],{"className":1736,"style":708},[707],[572,1738,681],{"className":1739},[712],[572,1741],{"className":1742,"style":708},[707],[572,1744,1746,1749,1778,1781,1784],{"className":1745},[614],[572,1747],{"className":1748,"style":619},[618],[572,1750,1752,1755],{"className":1751},[623],[572,1753,806],{"className":1754},[623],[572,1756,1758],{"className":1757},[631],[572,1759,1761],{"className":1760},[635],[572,1762,1764],{"className":1763},[639],[572,1765,1767],{"className":1766,"style":619},[643],[572,1768,1769,1772],{"style":646},[572,1770],{"className":1771,"style":651},[650],[572,1773,1775],{"className":1774},[655,656,657,658],[572,1776,600],{"className":1777},[623,658],[572,1779],{"className":1780,"style":935},[707],[572,1782,863],{"className":1783},[939],[572,1785],{"className":1786,"style":935},[707],[572,1788,1790,1793],{"className":1789},[614],[572,1791],{"className":1792,"style":700},[618],[572,1794,906],{"className":1795},[623],[1521,1797,1798,1799,751],{},"Oberfläche und Volumen verwechseln. Das Volumen ist ",[572,1800,1802,1825],{"className":1801},[575],[572,1803,1805],{"className":1804},[579],[581,1806,1807],{"xmlns":583},[585,1808,1809,1822],{},[588,1810,1811,1814,1816],{},[594,1812,1813],{},"V",[679,1815,863],{},[591,1817,1818,1820],{},[594,1819,596],{},[598,1821,806],{},[602,1823,1824],{"encoding":604},"V = a^3",[572,1826,1828,1846],{"className":1827,"ariaHidden":610},[609],[572,1829,1831,1834,1837,1840,1843],{"className":1830},[614],[572,1832],{"className":1833,"style":927},[618],[572,1835,1813],{"className":1836,"style":708},[623,627],[572,1838],{"className":1839,"style":935},[707],[572,1841,863],{"className":1842},[939],[572,1844],{"className":1845,"style":935},[707],[572,1847,1849,1852],{"className":1848},[614],[572,1850],{"className":1851,"style":619},[618],[572,1853,1855,1858],{"className":1854},[623],[572,1856,596],{"className":1857},[623,627],[572,1859,1861],{"className":1860},[631],[572,1862,1864],{"className":1863},[635],[572,1865,1867],{"className":1866},[639],[572,1868,1870],{"className":1869,"style":619},[643],[572,1871,1872,1875],{"style":646},[572,1873],{"className":1874,"style":651},[650],[572,1876,1878],{"className":1877},[655,656,657,658],[572,1879,806],{"className":1880},[623,658],{"title":1882,"searchDepth":1883,"depth":1883,"links":1884},"",2,[1885,1886,1887],{"id":560,"depth":1883,"text":561},{"id":787,"depth":1883,"text":788},{"id":1515,"depth":1883,"text":1516},[1889,1892,1894],{"lhs":1890,"rhs":1891},"2 * (a*a + a*a + a*a)","6 * a^2",{"lhs":1893,"rhs":906},"6 * 3^2",{"lhs":1895,"rhs":1896},"6 * 2.5^2","37.5",null,"md",{"caption":1900,"x":1901,"y":1904,"items":1907},"Würfel mit der Kantenlänge a; die drei sichtbaren der sechs gleichen Quadrate sind hervorgehoben",[1902,1903],-0.6,4.1,[1905,1906],-0.65,3.6,[1908,1919,1927,1934,1939,1942,1945,1948,1951,1954,1957,1960,1963,1967,1970,1973,1977,1980],{"type":1909,"points":1910,"fill":1917,"style":1918},"polygon",[1911,1913,1915,1916],[1912,1912],0,[1914,1912],2.4,[1914,1914],[1912,1914],true,"muted",{"type":1909,"points":1920,"fill":1917,"style":1918},[1921,1922,1924,1926],[1914,1912],[1906,1923],0.84,[1906,1925],3.24,[1914,1914],{"type":1909,"points":1928,"fill":1917,"style":1918},[1929,1930,1931,1932],[1912,1914],[1914,1914],[1906,1925],[1933,1925],1.2,{"type":1935,"from":1936,"to":1937,"style":1938},"segment",[1912,1912],[1914,1912],"main",{"type":1935,"from":1940,"to":1941,"style":1938},[1914,1912],[1914,1914],{"type":1935,"from":1943,"to":1944,"style":1938},[1914,1914],[1912,1914],{"type":1935,"from":1946,"to":1947,"style":1938},[1912,1914],[1912,1912],{"type":1935,"from":1949,"to":1950,"style":1938},[1914,1912],[1906,1923],{"type":1935,"from":1952,"to":1953,"style":1938},[1914,1914],[1906,1925],{"type":1935,"from":1955,"to":1956,"style":1938},[1912,1914],[1933,1925],{"type":1935,"from":1958,"to":1959,"style":1938},[1906,1923],[1906,1925],{"type":1935,"from":1961,"to":1962,"style":1938},[1906,1925],[1933,1925],{"type":1935,"from":1964,"to":1965,"style":1966},[1933,1923],[1912,1912],"dashed",{"type":1935,"from":1968,"to":1969,"style":1966},[1933,1923],[1906,1923],{"type":1935,"from":1971,"to":1972,"style":1966},[1933,1923],[1933,1925],{"type":1974,"at":1975,"text":596},"label",[1933,1976],-0.35,{"type":1974,"at":1978,"text":596},[1979,1933],2.68,{"type":1974,"at":1981,"text":596},[1982,1983],3.3,0.22,"\u003Csvg 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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>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-wuerfel",[],[1993,1994,1995],"cube-volume","square-area","cuboid-surface",{"title":548,"description":1882},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-wuerfel","Die Oberfläche eines Würfels besteht aus sechs gleichen Quadraten, also 6 mal a².",[2000,2001,2002,2003],"oberfläche","würfel","fläche","körper",[2005,2008],{"symbol":860,"meaning":2006,"symbolHtml":2007},"Oberflächeninhalt, die Fläche aller sechs Seiten zusammen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O\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:0.0278em;\">O\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":596,"meaning":2009,"symbolHtml":2010},"Kantenlänge des Würfels","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","YuphDIBdzOCelg2G5WtK92uPKkIbDoGAMkaTbcc7Fbk",[2013,2016,2019],{"stem":2014,"title":2015,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-quadrat","Flächeninhalt eines Quadrats",{"stem":2017,"title":2018,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-quader","Oberfläche eines Quaders",{"stem":2020,"title":2021,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-wuerfel","Volumen eines Würfels",1793824269593]