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",[572,1095,1097,1123],{"className":1096},[575],[572,1098,1100],{"className":1099},[579],[581,1101,1102],{"xmlns":583},[585,1103,1104,1120],{},[588,1105,1106,1108,1110,1116],{},[591,1107,896],{},[647,1109,877],{},[634,1111,1112,1114],{},[591,1113,593],{},[640,1115,885],{},[637,1117,1118],{},[640,1119,642],{},[595,1121,1122],{"encoding":597},"h = \\frac{a}{2}\\sqrt{3}",[572,1124,1126,1144],{"className":1125,"ariaHidden":602},[601],[572,1127,1129,1132,1135,1138,1141],{"className":1128},[606],[572,1130],{"className":1131,"style":1036},[610],[572,1133,896],{"className":1134},[615,616],[572,1136],{"className":1137,"style":821},[820],[572,1139,877],{"className":1140},[825],[572,1142],{"className":1143,"style":821},[820],[572,1145,1147,1151,1220],{"className":1146},[606],[572,1148],{"className":1149,"style":1150},[610],"height:1.2522em;vertical-align:-0.345em;",[572,1152,1154,1157,1217],{"className":1153},[615],[572,1155],{"className":1156},[672,673],[572,1158,1160],{"className":1159},[634],[572,1161,1163,1209],{"className":1162},[680,681],[572,1164,1166,1206],{"className":1165},[685],[572,1167,1170,1184,1192],{"className":1168,"style":1169},[689],"height:0.6954em;",[572,1171,1172,1175],{"style":693},[572,1173],{"className":1174,"style":698},[697],[572,1176,1178],{"className":1177},[702,703,704,705],[572,1179,1181],{"className":1180},[615,705],[572,1182,885],{"className":1183},[615,705],[572,1185,1186,1189],{"style":714},[572,1187],{"className":1188,"style":698},[697],[572,1190],{"className":1191,"style":722},[721],[572,1193,1194,1197],{"style":972},[572,1195],{"className":1196,"style":698},[697],[572,1198,1200],{"className":1199},[702,703,704,705],[572,1201,1203],{"className":1202},[615,705],[572,1204,593],{"className":1205},[615,616,705],[572,1207,791],{"className":1208},[790],[572,1210,1212],{"className":1211},[685],[572,1213,1215],{"className":1214,"style":810},[689],[572,1216],{},[572,1218],{"className":1219},[816,673],[572,1221,1223],{"className":1222},[615,738],[572,1224,1226,1261],{"className":1225},[680,681],[572,1227,1229,1258],{"className":1228},[685],[572,1230,1233,1245],{"className":1231,"style":1232},[689],"height:0.9072em;",[572,1234,1236,1239],{"className":1235,"style":753},[752],[572,1237],{"className":1238,"style":698},[697],[572,1240,1242],{"className":1241,"style":760},[615],[572,1243,642],{"className":1244},[615],[572,1246,1248,1251],{"style":1247},"top:-2.8672em;",[572,1249],{"className":1250,"style":698},[697],[572,1252,1254],{"className":1253,"style":774},[773],[776,1255,1256],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,1257],{"d":786},[572,1259,791],{"className":1260},[790],[572,1262,1264],{"className":1263},[685],[572,1265,1268],{"className":1266,"style":1267},[689],"height:0.1328em;",[572,1269],{},":",[572,1272,1275],{"className":1273},[1274],"katex-display",[572,1276,1278,1334],{"className":1277},[575],[572,1279,1281],{"className":1280},[579],[581,1282,1284],{"xmlns":583,"display":1283},"block",[585,1285,1286,1331],{},[588,1287,1288,1290,1292,1298,1300,1302,1304,1310,1314,1316,1327],{},[591,1289,874],{},[647,1291,877],{},[634,1293,1294,1296],{},[640,1295,882],{},[640,1297,885],{},[647,1299,888],{},[591,1301,593],{},[647,1303,888],{},[634,1305,1306,1308],{},[591,1307,593],{},[640,1309,885],{},[637,1311,1312],{},[640,1313,642],{},[647,1315,877],{},[634,1317,1318,1325],{},[1319,1320,1321,1323],"msup",{},[591,1322,593],{},[640,1324,885],{},[640,1326,645],{},[637,1328,1329],{},[640,1330,642],{},[595,1332,1333],{"encoding":597},"A = \\frac{1}{2} \\cdot a \\cdot \\frac{a}{2}\\sqrt{3} = \\frac{a^2}{4}\\sqrt{3}",[572,1335,1337,1355,1437,1456,1585],{"className":1336,"ariaHidden":602},[601],[572,1338,1340,1343,1346,1349,1352],{"className":1339},[606],[572,1341],{"className":1342,"style":909},[610],[572,1344,874],{"className":1345},[615,616],[572,1347],{"className":1348,"style":821},[820],[572,1350,877],{"className":1351},[825],[572,1353],{"className":1354,"style":821},[820],[572,1356,1358,1362,1428,1431,1434],{"className":1357},[606],[572,1359],{"className":1360,"style":1361},[610],"height:2.0074em;vertical-align:-0.686em;",[572,1363,1365,1368,1425],{"className":1364},[615],[572,1366],{"className":1367},[672,673],[572,1369,1371],{"className":1370},[634],[572,1372,1374,1416],{"className":1373},[680,681],[572,1375,1377,1413],{"className":1376},[685],[572,1378,1381,1393,1401],{"className":1379,"style":1380},[689],"height:1.3214em;",[572,1382,1384,1387],{"style":1383},"top:-2.314em;",[572,1385],{"className":1386,"style":698},[697],[572,1388,1390],{"className":1389},[615],[572,1391,885],{"className":1392},[615],[572,1394,1395,1398],{"style":714},[572,1396],{"className":1397,"style":698},[697],[572,1399],{"className":1400,"style":722},[721],[572,1402,1404,1407],{"style":1403},"top:-3.677em;",[572,1405],{"className":1406,"style":698},[697],[572,1408,1410],{"className":1409},[615],[572,1411,882],{"className":1412},[615],[572,1414,791],{"className":1415},[790],[572,1417,1419],{"className":1418},[685],[572,1420,1423],{"className":1421,"style":1422},[689],"height:0.686em;",[572,1424],{},[572,1426],{"className":1427},[816,673],[572,1429],{"className":1430,"style":1002},[820],[572,1432,888],{"className":1433},[1006],[572,1435],{"className":1436,"style":1002},[820],[572,1438,1440,1444,1447,1450,1453],{"className":1439},[606],[572,1441],{"className":1442,"style":1443},[610],"height:0.4445em;",[572,1445,593],{"className":1446},[615,616],[572,1448],{"className":1449,"style":1002},[820],[572,1451,888],{"className":1452},[1006],[572,1454],{"className":1455,"style":1002},[820],[572,1457,1459,1463,1526,1576,1579,1582],{"className":1458},[606],[572,1460],{"className":1461,"style":1462},[610],"height:1.7936em;vertical-align:-0.686em;",[572,1464,1466,1469,1523],{"className":1465},[615],[572,1467],{"className":1468},[672,673],[572,1470,1472],{"className":1471},[634],[572,1473,1475,1515],{"className":1474},[680,681],[572,1476,1478,1512],{"className":1477},[685],[572,1479,1482,1493,1501],{"className":1480,"style":1481},[689],"height:1.1076em;",[572,1483,1484,1487],{"style":1383},[572,1485],{"className":1486,"style":698},[697],[572,1488,1490],{"className":1489},[615],[572,1491,885],{"className":1492},[615],[572,1494,1495,1498],{"style":714},[572,1496],{"className":1497,"style":698},[697],[572,1499],{"className":1500,"style":722},[721],[572,1502,1503,1506],{"style":1403},[572,1504],{"className":1505,"style":698},[697],[572,1507,1509],{"className":1508},[615],[572,1510,593],{"className":1511},[615,616],[572,1513,791],{"className":1514},[790],[572,1516,1518],{"className":1517},[685],[572,1519,1521],{"className":1520,"style":1422},[689],[572,1522],{},[572,1524],{"className":1525},[816,673],[572,1527,1529],{"className":1528},[615,738],[572,1530,1532,1567],{"className":1531},[680,681],[572,1533,1535,1564],{"className":1534},[685],[572,1536,1539,1551],{"className":1537,"style":1538},[689],"height:0.9561em;",[572,1540,1542,1545],{"className":1541,"style":753},[752],[572,1543],{"className":1544,"style":698},[697],[572,1546,1548],{"className":1547,"style":760},[615],[572,1549,642],{"className":1550},[615],[572,1552,1554,1557],{"style":1553},"top:-2.9161em;",[572,1555],{"className":1556,"style":698},[697],[572,1558,1560],{"className":1559,"style":774},[773],[776,1561,1562],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,1563],{"d":786},[572,1565,791],{"className":1566},[790],[572,1568,1570],{"className":1569},[685],[572,1571,1574],{"className":1572,"style":1573},[689],"height:0.0839em;",[572,1575],{},[572,1577],{"className":1578,"style":821},[820],[572,1580,877],{"className":1581},[825],[572,1583],{"className":1584,"style":821},[820],[572,1586,1588,1592,1685],{"className":1587},[606],[572,1589],{"className":1590,"style":1591},[610],"height:2.1771em;vertical-align:-0.686em;",[572,1593,1595,1598,1682],{"className":1594},[615],[572,1596],{"className":1597},[672,673],[572,1599,1601],{"className":1600},[634],[572,1602,1604,1674],{"className":1603},[680,681],[572,1605,1607,1671],{"className":1606},[685],[572,1608,1611,1622,1630],{"className":1609,"style":1610},[689],"height:1.4911em;",[572,1612,1613,1616],{"style":1383},[572,1614],{"className":1615,"style":698},[697],[572,1617,1619],{"className":1618},[615],[572,1620,645],{"className":1621},[615],[572,1623,1624,1627],{"style":714},[572,1625],{"className":1626,"style":698},[697],[572,1628],{"className":1629,"style":722},[721],[572,1631,1632,1635],{"style":1403},[572,1633],{"className":1634,"style":698},[697],[572,1636,1638],{"className":1637},[615],[572,1639,1641,1644],{"className":1640},[615],[572,1642,593],{"className":1643},[615,616],[572,1645,1648],{"className":1646},[1647],"msupsub",[572,1649,1651],{"className":1650},[680],[572,1652,1654],{"className":1653},[685],[572,1655,1658],{"className":1656,"style":1657},[689],"height:0.8141em;",[572,1659,1661,1665],{"style":1660},"top:-3.063em;margin-right:0.05em;",[572,1662],{"className":1663,"style":1664},[697],"height:2.7em;",[572,1666,1668],{"className":1667},[702,703,704,705],[572,1669,885],{"className":1670},[615,705],[572,1672,791],{"className":1673},[790],[572,1675,1677],{"className":1676},[685],[572,1678,1680],{"className":1679,"style":1422},[689],[572,1681],{},[572,1683],{"className":1684},[816,673],[572,1686,1688],{"className":1687},[615,738],[572,1689,1691,1724],{"className":1690},[680,681],[572,1692,1694,1721],{"className":1693},[685],[572,1695,1697,1709],{"className":1696,"style":1538},[689],[572,1698,1700,1703],{"className":1699,"style":753},[752],[572,1701],{"className":1702,"style":698},[697],[572,1704,1706],{"className":1705,"style":760},[615],[572,1707,642],{"className":1708},[615],[572,1710,1711,1714],{"style":1553},[572,1712],{"className":1713,"style":698},[697],[572,1715,1717],{"className":1716,"style":774},[773],[776,1718,1719],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,1720],{"d":786},[572,1722,791],{"className":1723},[790],[572,1725,1727],{"className":1726},[685],[572,1728,1730],{"className":1729,"style":1573},[689],[572,1731],{},[558,1733,1735],{"id":1734},"beispiele","Beispiele",[563,1737,1738,1739,1270],{},"Ein gleichseitiges Dreieck hat die Seitenlänge ",[572,1740,1742,1764],{"className":1741},[575],[572,1743,1745],{"className":1744},[579],[581,1746,1747],{"xmlns":583},[585,1748,1749,1761],{},[588,1750,1751,1754,1758],{},[640,1752,1753],{},"6",[1755,1756,1757],"mtext",{}," ",[1755,1759,1760],{},"cm",[595,1762,1763],{"encoding":597},"6\\,\\text{cm}",[572,1765,1767],{"className":1766,"ariaHidden":602},[601],[572,1768,1770,1774,1777,1781],{"className":1769},[606],[572,1771],{"className":1772,"style":1773},[610],"height:0.6444em;",[572,1775,1753],{"className":1776},[615],[572,1778],{"className":1779,"style":1780},[820],"margin-right:0.1667em;",[572,1782,1785],{"className":1783},[615,1784],"text",[572,1786,1760],{"className":1787},[615],[572,1789,1791],{"className":1790},[1274],[572,1792,1794,1862],{"className":1793},[575],[572,1795,1797],{"className":1796},[579],[581,1798,1799],{"xmlns":583,"display":1283},[585,1800,1801,1859],{},[588,1802,1803,1805,1807,1817,1821,1823,1829,1831,1834,1838,1840,1846,1848,1851,1853],{},[591,1804,874],{},[647,1806,877],{},[634,1808,1809,1815],{},[1319,1810,1811,1813],{},[640,1812,1753],{},[640,1814,885],{},[640,1816,645],{},[637,1818,1819],{},[640,1820,642],{},[1755,1822,1757],{},[1319,1824,1825,1827],{},[1755,1826,1760],{},[640,1828,885],{},[647,1830,877],{},[640,1832,1833],{},"9",[637,1835,1836],{},[640,1837,642],{},[1755,1839,1757],{},[1319,1841,1842,1844],{},[1755,1843,1760],{},[640,1845,885],{},[647,1847,649],{},[640,1849,1850],{},"15,59",[1755,1852,1757],{},[1319,1854,1855,1857],{},[1755,1856,1760],{},[640,1858,885],{},[595,1860,1861],{"encoding":597},"A = \\frac{6^2}{4}\\sqrt{3}\\,\\text{cm}^2 = 9\\sqrt{3}\\,\\text{cm}^2 \\approx 15{,}59\\,\\text{cm}^2",[572,1863,1865,1883,2070,2171],{"className":1864,"ariaHidden":602},[601],[572,1866,1868,1871,1874,1877,1880],{"className":1867},[606],[572,1869],{"className":1870,"style":909},[610],[572,1872,874],{"className":1873},[615,616],[572,1875],{"className":1876,"style":821},[820],[572,1878,877],{"className":1879},[825],[572,1881],{"className":1882,"style":821},[820],[572,1884,1886,1889,1977,2024,2027,2061,2064,2067],{"className":1885},[606],[572,1887],{"className":1888,"style":1591},[610],[572,1890,1892,1895,1974],{"className":1891},[615],[572,1893],{"className":1894},[672,673],[572,1896,1898],{"className":1897},[634],[572,1899,1901,1966],{"className":1900},[680,681],[572,1902,1904,1963],{"className":1903},[685],[572,1905,1907,1918,1926],{"className":1906,"style":1610},[689],[572,1908,1909,1912],{"style":1383},[572,1910],{"className":1911,"style":698},[697],[572,1913,1915],{"className":1914},[615],[572,1916,645],{"className":1917},[615],[572,1919,1920,1923],{"style":714},[572,1921],{"className":1922,"style":698},[697],[572,1924],{"className":1925,"style":722},[721],[572,1927,1928,1931],{"style":1403},[572,1929],{"className":1930,"style":698},[697],[572,1932,1934],{"className":1933},[615],[572,1935,1937,1940],{"className":1936},[615],[572,1938,1753],{"className":1939},[615],[572,1941,1943],{"className":1942},[1647],[572,1944,1946],{"className":1945},[680],[572,1947,1949],{"className":1948},[685],[572,1950,1952],{"className":1951,"style":1657},[689],[572,1953,1954,1957],{"style":1660},[572,1955],{"className":1956,"style":1664},[697],[572,1958,1960],{"className":1959},[702,703,704,705],[572,1961,885],{"className":1962},[615,705],[572,1964,791],{"className":1965},[790],[572,1967,1969],{"className":1968},[685],[572,1970,1972],{"className":1971,"style":1422},[689],[572,1973],{},[572,1975],{"className":1976},[816,673],[572,1978,1980],{"className":1979},[615,738],[572,1981,1983,2016],{"className":1982},[680,681],[572,1984,1986,2013],{"className":1985},[685],[572,1987,1989,2001],{"className":1988,"style":1538},[689],[572,1990,1992,1995],{"className":1991,"style":753},[752],[572,1993],{"className":1994,"style":698},[697],[572,1996,1998],{"className":1997,"style":760},[615],[572,1999,642],{"className":2000},[615],[572,2002,2003,2006],{"style":1553},[572,2004],{"className":2005,"style":698},[697],[572,2007,2009],{"className":2008,"style":774},[773],[776,2010,2011],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,2012],{"d":786},[572,2014,791],{"className":2015},[790],[572,2017,2019],{"className":2018},[685],[572,2020,2022],{"className":2021,"style":1573},[689],[572,2023],{},[572,2025],{"className":2026,"style":1780},[820],[572,2028,2030,2036],{"className":2029},[615],[572,2031,2033],{"className":2032},[615,1784],[572,2034,1760],{"className":2035},[615],[572,2037,2039],{"className":2038},[1647],[572,2040,2042],{"className":2041},[680],[572,2043,2045],{"className":2044},[685],[572,2046,2049],{"className":2047,"style":2048},[689],"height:0.8641em;",[572,2050,2052,2055],{"style":2051},"top:-3.113em;margin-right:0.05em;",[572,2053],{"className":2054,"style":1664},[697],[572,2056,2058],{"className":2057},[702,703,704,705],[572,2059,885],{"className":2060},[615,705],[572,2062],{"className":2063,"style":821},[820],[572,2065,877],{"className":2066},[825],[572,2068],{"className":2069,"style":821},[820],[572,2071,2073,2077,2080,2127,2130,2162,2165,2168],{"className":2072},[606],[572,2074],{"className":2075,"style":2076},[610],"height:1.04em;vertical-align:-0.0839em;",[572,2078,1833],{"className":2079},[615],[572,2081,2083],{"className":2082},[615,738],[572,2084,2086,2119],{"className":2085},[680,681],[572,2087,2089,2116],{"className":2088},[685],[572,2090,2092,2104],{"className":2091,"style":1538},[689],[572,2093,2095,2098],{"className":2094,"style":753},[752],[572,2096],{"className":2097,"style":698},[697],[572,2099,2101],{"className":2100,"style":760},[615],[572,2102,642],{"className":2103},[615],[572,2105,2106,2109],{"style":1553},[572,2107],{"className":2108,"style":698},[697],[572,2110,2112],{"className":2111,"style":774},[773],[776,2113,2114],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,2115],{"d":786},[572,2117,791],{"className":2118},[790],[572,2120,2122],{"className":2121},[685],[572,2123,2125],{"className":2124,"style":1573},[689],[572,2126],{},[572,2128],{"className":2129,"style":1780},[820],[572,2131,2133,2139],{"className":2132},[615],[572,2134,2136],{"className":2135},[615,1784],[572,2137,1760],{"className":2138},[615],[572,2140,2142],{"className":2141},[1647],[572,2143,2145],{"className":2144},[680],[572,2146,2148],{"className":2147},[685],[572,2149,2151],{"className":2150,"style":2048},[689],[572,2152,2153,2156],{"style":2051},[572,2154],{"className":2155,"style":1664},[697],[572,2157,2159],{"className":2158},[702,703,704,705],[572,2160,885],{"className":2161},[615,705],[572,2163],{"className":2164,"style":821},[820],[572,2166,649],{"className":2167},[825],[572,2169],{"className":2170,"style":821},[820],[572,2172,2174,2178,2182,2188,2192,2195],{"className":2173},[606],[572,2175],{"className":2176,"style":2177},[610],"height:1.0585em;vertical-align:-0.1944em;",[572,2179,2181],{"className":2180},[615],"15",[572,2183,2185],{"className":2184},[615],[572,2186,847],{"className":2187},[846],[572,2189,2191],{"className":2190},[615],"59",[572,2193],{"className":2194,"style":1780},[820],[572,2196,2198,2204],{"className":2197},[615],[572,2199,2201],{"className":2200},[615,1784],[572,2202,1760],{"className":2203},[615],[572,2205,2207],{"className":2206},[1647],[572,2208,2210],{"className":2209},[680],[572,2211,2213],{"className":2212},[685],[572,2214,2216],{"className":2215,"style":2048},[689],[572,2217,2218,2221],{"style":2051},[572,2219],{"className":2220,"style":1664},[697],[572,2222,2224],{"className":2223},[702,703,704,705],[572,2225,885],{"className":2226},[615,705],[563,2228,2229,2230,1270],{},"Ein dreieckiges Verkehrsschild hat die Seitenlänge ",[572,2231,2233,2253],{"className":2232},[575],[572,2234,2236],{"className":2235},[579],[581,2237,2238],{"xmlns":583},[585,2239,2240,2250],{},[588,2241,2242,2245,2247],{},[640,2243,2244],{},"10",[1755,2246,1757],{},[1755,2248,2249],{},"dm",[595,2251,2252],{"encoding":597},"10\\,\\text{dm}",[572,2254,2256],{"className":2255,"ariaHidden":602},[601],[572,2257,2259,2262,2265,2268],{"className":2258},[606],[572,2260],{"className":2261,"style":1036},[610],[572,2263,2244],{"className":2264},[615],[572,2266],{"className":2267,"style":1780},[820],[572,2269,2271],{"className":2270},[615,1784],[572,2272,2249],{"className":2273},[615],[572,2275,2277],{"className":2276},[1274],[572,2278,2280,2348],{"className":2279},[575],[572,2281,2283],{"className":2282},[579],[581,2284,2285],{"xmlns":583,"display":1283},[585,2286,2287,2345],{},[588,2288,2289,2291,2293,2303,2307,2309,2315,2317,2320,2324,2326,2332,2334,2337,2339],{},[591,2290,874],{},[647,2292,877],{},[634,2294,2295,2301],{},[1319,2296,2297,2299],{},[640,2298,2244],{},[640,2300,885],{},[640,2302,645],{},[637,2304,2305],{},[640,2306,642],{},[1755,2308,1757],{},[1319,2310,2311,2313],{},[1755,2312,2249],{},[640,2314,885],{},[647,2316,877],{},[640,2318,2319],{},"25",[637,2321,2322],{},[640,2323,642],{},[1755,2325,1757],{},[1319,2327,2328,2330],{},[1755,2329,2249],{},[640,2331,885],{},[647,2333,649],{},[640,2335,2336],{},"43,3",[1755,2338,1757],{},[1319,2340,2341,2343],{},[1755,2342,2249],{},[640,2344,885],{},[595,2346,2347],{"encoding":597},"A = \\frac{10^2}{4}\\sqrt{3}\\,\\text{dm}^2 = 25\\sqrt{3}\\,\\text{dm}^2 \\approx 43{,}3\\,\\text{dm}^2",[572,2349,2351,2369,2559,2659],{"className":2350,"ariaHidden":602},[601],[572,2352,2354,2357,2360,2363,2366],{"className":2353},[606],[572,2355],{"className":2356,"style":909},[610],[572,2358,874],{"className":2359},[615,616],[572,2361],{"className":2362,"style":821},[820],[572,2364,877],{"className":2365},[825],[572,2367],{"className":2368,"style":821},[820],[572,2370,2372,2375,2466,2513,2516,2550,2553,2556],{"className":2371},[606],[572,2373],{"className":2374,"style":1591},[610],[572,2376,2378,2381,2463],{"className":2377},[615],[572,2379],{"className":2380},[672,673],[572,2382,2384],{"className":2383},[634],[572,2385,2387,2455],{"className":2386},[680,681],[572,2388,2390,2452],{"className":2389},[685],[572,2391,2393,2404,2412],{"className":2392,"style":1610},[689],[572,2394,2395,2398],{"style":1383},[572,2396],{"className":2397,"style":698},[697],[572,2399,2401],{"className":2400},[615],[572,2402,645],{"className":2403},[615],[572,2405,2406,2409],{"style":714},[572,2407],{"className":2408,"style":698},[697],[572,2410],{"className":2411,"style":722},[721],[572,2413,2414,2417],{"style":1403},[572,2415],{"className":2416,"style":698},[697],[572,2418,2420,2423],{"className":2419},[615],[572,2421,882],{"className":2422},[615],[572,2424,2426,2429],{"className":2425},[615],[572,2427,839],{"className":2428},[615],[572,2430,2432],{"className":2431},[1647],[572,2433,2435],{"className":2434},[680],[572,2436,2438],{"className":2437},[685],[572,2439,2441],{"className":2440,"style":1657},[689],[572,2442,2443,2446],{"style":1660},[572,2444],{"className":2445,"style":1664},[697],[572,2447,2449],{"className":2448},[702,703,704,705],[572,2450,885],{"className":2451},[615,705],[572,2453,791],{"className":2454},[790],[572,2456,2458],{"className":2457},[685],[572,2459,2461],{"className":2460,"style":1422},[689],[572,2462],{},[572,2464],{"className":2465},[816,673],[572,2467,2469],{"className":2468},[615,738],[572,2470,2472,2505],{"className":2471},[680,681],[572,2473,2475,2502],{"className":2474},[685],[572,2476,2478,2490],{"className":2477,"style":1538},[689],[572,2479,2481,2484],{"className":2480,"style":753},[752],[572,2482],{"className":2483,"style":698},[697],[572,2485,2487],{"className":2486,"style":760},[615],[572,2488,642],{"className":2489},[615],[572,2491,2492,2495],{"style":1553},[572,2493],{"className":2494,"style":698},[697],[572,2496,2498],{"className":2497,"style":774},[773],[776,2499,2500],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,2501],{"d":786},[572,2503,791],{"className":2504},[790],[572,2506,2508],{"className":2507},[685],[572,2509,2511],{"className":2510,"style":1573},[689],[572,2512],{},[572,2514],{"className":2515,"style":1780},[820],[572,2517,2519,2525],{"className":2518},[615],[572,2520,2522],{"className":2521},[615,1784],[572,2523,2249],{"className":2524},[615],[572,2526,2528],{"className":2527},[1647],[572,2529,2531],{"className":2530},[680],[572,2532,2534],{"className":2533},[685],[572,2535,2538],{"className":2536,"style":2537},[689],"height:0.8984em;",[572,2539,2541,2544],{"style":2540},"top:-3.1473em;margin-right:0.05em;",[572,2542],{"className":2543,"style":1664},[697],[572,2545,2547],{"className":2546},[702,703,704,705],[572,2548,885],{"className":2549},[615,705],[572,2551],{"className":2552,"style":821},[820],[572,2554,877],{"className":2555},[825],[572,2557],{"className":2558,"style":821},[820],[572,2560,2562,2565,2568,2615,2618,2650,2653,2656],{"className":2561},[606],[572,2563],{"className":2564,"style":2076},[610],[572,2566,2319],{"className":2567},[615],[572,2569,2571],{"className":2570},[615,738],[572,2572,2574,2607],{"className":2573},[680,681],[572,2575,2577,2604],{"className":2576},[685],[572,2578,2580,2592],{"className":2579,"style":1538},[689],[572,2581,2583,2586],{"className":2582,"style":753},[752],[572,2584],{"className":2585,"style":698},[697],[572,2587,2589],{"className":2588,"style":760},[615],[572,2590,642],{"className":2591},[615],[572,2593,2594,2597],{"style":1553},[572,2595],{"className":2596,"style":698},[697],[572,2598,2600],{"className":2599,"style":774},[773],[776,2601,2602],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,2603],{"d":786},[572,2605,791],{"className":2606},[790],[572,2608,2610],{"className":2609},[685],[572,2611,2613],{"className":2612,"style":1573},[689],[572,2614],{},[572,2616],{"className":2617,"style":1780},[820],[572,2619,2621,2627],{"className":2620},[615],[572,2622,2624],{"className":2623},[615,1784],[572,2625,2249],{"className":2626},[615],[572,2628,2630],{"className":2629},[1647],[572,2631,2633],{"className":2632},[680],[572,2634,2636],{"className":2635},[685],[572,2637,2639],{"className":2638,"style":2537},[689],[572,2640,2641,2644],{"style":2540},[572,2642],{"className":2643,"style":1664},[697],[572,2645,2647],{"className":2646},[702,703,704,705],[572,2648,885],{"className":2649},[615,705],[572,2651],{"className":2652,"style":821},[820],[572,2654,649],{"className":2655},[825],[572,2657],{"className":2658,"style":821},[820],[572,2660,2662,2666,2670,2676,2679,2682],{"className":2661},[606],[572,2663],{"className":2664,"style":2665},[610],"height:1.0929em;vertical-align:-0.1944em;",[572,2667,2669],{"className":2668},[615],"43",[572,2671,2673],{"className":2672},[615],[572,2674,847],{"className":2675},[846],[572,2677,642],{"className":2678},[615],[572,2680],{"className":2681,"style":1780},[820],[572,2683,2685,2691],{"className":2684},[615],[572,2686,2688],{"className":2687},[615,1784],[572,2689,2249],{"className":2690},[615],[572,2692,2694],{"className":2693},[1647],[572,2695,2697],{"className":2696},[680],[572,2698,2700],{"className":2699},[685],[572,2701,2703],{"className":2702,"style":2537},[689],[572,2704,2705,2708],{"style":2540},[572,2706],{"className":2707,"style":1664},[697],[572,2709,2711],{"className":2710},[702,703,704,705],[572,2712,885],{"className":2713},[615,705],[558,2715,2717],{"id":2716},"typische-fehler","Typische Fehler",[2719,2720,2721,2951,3104],"ul",{},[2722,2723,2724,2725,2753,2754,2782,2783,2868,2869,2950],"li",{},"Durch ",[572,2726,2728,2741],{"className":2727},[575],[572,2729,2731],{"className":2730},[579],[581,2732,2733],{"xmlns":583},[585,2734,2735,2739],{},[588,2736,2737],{},[640,2738,885],{},[595,2740,885],{"encoding":597},[572,2742,2744],{"className":2743,"ariaHidden":602},[601],[572,2745,2747,2750],{"className":2746},[606],[572,2748],{"className":2749,"style":1773},[610],[572,2751,885],{"className":2752},[615]," statt durch ",[572,2755,2757,2770],{"className":2756},[575],[572,2758,2760],{"className":2759},[579],[581,2761,2762],{"xmlns":583},[585,2763,2764,2768],{},[588,2765,2766],{},[640,2767,645],{},[595,2769,645],{"encoding":597},[572,2771,2773],{"className":2772,"ariaHidden":602},[601],[572,2774,2776,2779],{"className":2775},[606],[572,2777],{"className":2778,"style":1773},[610],[572,2780,645],{"className":2781},[615]," teilen. Das ergibt das Doppelte, im ersten Beispiel ",[572,2784,2786,2809],{"className":2785},[575],[572,2787,2789],{"className":2788},[579],[581,2790,2791],{"xmlns":583},[585,2792,2793,2806],{},[588,2794,2795,2798,2800],{},[640,2796,2797],{},"31,18",[1755,2799,1757],{},[1319,2801,2802,2804],{},[1755,2803,1760],{},[640,2805,885],{},[595,2807,2808],{"encoding":597},"31{,}18\\,\\text{cm}^2",[572,2810,2812],{"className":2811,"ariaHidden":602},[601],[572,2813,2815,2819,2823,2829,2833,2836],{"className":2814},[606],[572,2816],{"className":2817,"style":2818},[610],"height:1.0085em;vertical-align:-0.1944em;",[572,2820,2822],{"className":2821},[615],"31",[572,2824,2826],{"className":2825},[615],[572,2827,847],{"className":2828},[846],[572,2830,2832],{"className":2831},[615],"18",[572,2834],{"className":2835,"style":1780},[820],[572,2837,2839,2845],{"className":2838},[615],[572,2840,2842],{"className":2841},[615,1784],[572,2843,1760],{"className":2844},[615],[572,2846,2848],{"className":2847},[1647],[572,2849,2851],{"className":2850},[680],[572,2852,2854],{"className":2853},[685],[572,2855,2857],{"className":2856,"style":1657},[689],[572,2858,2859,2862],{"style":1660},[572,2860],{"className":2861,"style":1664},[697],[572,2863,2865],{"className":2864},[702,703,704,705],[572,2866,885],{"className":2867},[615,705]," statt ",[572,2870,2872,2894],{"className":2871},[575],[572,2873,2875],{"className":2874},[579],[581,2876,2877],{"xmlns":583},[585,2878,2879,2891],{},[588,2880,2881,2883,2885],{},[640,2882,1850],{},[1755,2884,1757],{},[1319,2886,2887,2889],{},[1755,2888,1760],{},[640,2890,885],{},[595,2892,2893],{"encoding":597},"15{,}59\\,\\text{cm}^2",[572,2895,2897],{"className":2896,"ariaHidden":602},[601],[572,2898,2900,2903,2906,2912,2915,2918],{"className":2899},[606],[572,2901],{"className":2902,"style":2818},[610],[572,2904,2181],{"className":2905},[615],[572,2907,2909],{"className":2908},[615],[572,2910,847],{"className":2911},[846],[572,2913,2191],{"className":2914},[615],[572,2916],{"className":2917,"style":1780},[820],[572,2919,2921,2927],{"className":2920},[615],[572,2922,2924],{"className":2923},[615,1784],[572,2925,1760],{"className":2926},[615],[572,2928,2930],{"className":2929},[1647],[572,2931,2933],{"className":2932},[680],[572,2934,2936],{"className":2935},[685],[572,2937,2939],{"className":2938,"style":1657},[689],[572,2940,2941,2944],{"style":1660},[572,2942],{"className":2943,"style":1664},[697],[572,2945,2947],{"className":2946},[702,703,704,705],[572,2948,885],{"className":2949},[615,705],".",[2722,2952,2953,2954,3103],{},"Die Seitenlänge nicht quadrieren: ",[572,2955,2957,2979],{"className":2956},[575],[572,2958,2960],{"className":2959},[579],[581,2961,2962],{"xmlns":583},[585,2963,2964,2976],{},[588,2965,2966,2972],{},[634,2967,2968,2970],{},[591,2969,593],{},[640,2971,645],{},[637,2973,2974],{},[640,2975,642],{},[595,2977,2978],{"encoding":597},"\\frac{a}{4}\\sqrt{3}",[572,2980,2982],{"className":2981,"ariaHidden":602},[601],[572,2983,2985,2988,3056],{"className":2984},[606],[572,2986],{"className":2987,"style":1150},[610],[572,2989,2991,2994,3053],{"className":2990},[615],[572,2992],{"className":2993},[672,673],[572,2995,2997],{"className":2996},[634],[572,2998,3000,3045],{"className":2999},[680,681],[572,3001,3003,3042],{"className":3002},[685],[572,3004,3006,3020,3028],{"className":3005,"style":1169},[689],[572,3007,3008,3011],{"style":693},[572,3009],{"className":3010,"style":698},[697],[572,3012,3014],{"className":3013},[702,703,704,705],[572,3015,3017],{"className":3016},[615,705],[572,3018,645],{"className":3019},[615,705],[572,3021,3022,3025],{"style":714},[572,3023],{"className":3024,"style":698},[697],[572,3026],{"className":3027,"style":722},[721],[572,3029,3030,3033],{"style":972},[572,3031],{"className":3032,"style":698},[697],[572,3034,3036],{"className":3035},[702,703,704,705],[572,3037,3039],{"className":3038},[615,705],[572,3040,593],{"className":3041},[615,616,705],[572,3043,791],{"className":3044},[790],[572,3046,3048],{"className":3047},[685],[572,3049,3051],{"className":3050,"style":810},[689],[572,3052],{},[572,3054],{"className":3055},[816,673],[572,3057,3059],{"className":3058},[615,738],[572,3060,3062,3095],{"className":3061},[680,681],[572,3063,3065,3092],{"className":3064},[685],[572,3066,3068,3080],{"className":3067,"style":1232},[689],[572,3069,3071,3074],{"className":3070,"style":753},[752],[572,3072],{"className":3073,"style":698},[697],[572,3075,3077],{"className":3076,"style":760},[615],[572,3078,642],{"className":3079},[615],[572,3081,3082,3085],{"style":1247},[572,3083],{"className":3084,"style":698},[697],[572,3086,3088],{"className":3087,"style":774},[773],[776,3089,3090],{"xmlns":778,"width":779,"height":780,"viewBox":781,"preserveAspectRatio":782},[784,3091],{"d":786},[572,3093,791],{"className":3094},[790],[572,3096,3098],{"className":3097},[685],[572,3099,3101],{"className":3100,"style":1267},[689],[572,3102],{}," ist keine Fläche.",[2722,3105,3106,3107,2950],{},"Die Formel für gleichschenklige Dreiecke verwenden. Dort sind nicht alle Seiten gleich, man braucht ",[572,3108,3110,3136],{"className":3109},[575],[572,3111,3113],{"className":3112},[579],[581,3114,3115],{"xmlns":583},[585,3116,3117,3133],{},[588,3118,3119,3121,3123,3129,3131],{},[591,3120,874],{},[647,3122,877],{},[634,3124,3125,3127],{},[640,3126,882],{},[640,3128,885],{},[591,3130,891],{},[591,3132,896],{},[595,3134,3135],{"encoding":597},"A = \\frac{1}{2} g h",[572,3137,3139,3157],{"className":3138,"ariaHidden":602},[601],[572,3140,3142,3145,3148,3151,3154],{"className":3141},[606],[572,3143],{"className":3144,"style":909},[610],[572,3146,874],{"className":3147},[615,616],[572,3149],{"className":3150,"style":821},[820],[572,3152,877],{"className":3153},[825],[572,3155],{"className":3156,"style":821},[820],[572,3158,3160,3163,3231,3234],{"className":3159},[606],[572,3161],{"className":3162,"style":928},[610],[572,3164,3166,3169,3228],{"className":3165},[615],[572,3167],{"className":3168},[672,673],[572,3170,3172],{"className":3171},[634],[572,3173,3175,3220],{"className":3174},[680,681],[572,3176,3178,3217],{"className":3177},[685],[572,3179,3181,3195,3203],{"className":3180,"style":947},[689],[572,3182,3183,3186],{"style":693},[572,3184],{"className":3185,"style":698},[697],[572,3187,3189],{"className":3188},[702,703,704,705],[572,3190,3192],{"className":3191},[615,705],[572,3193,885],{"className":3194},[615,705],[572,3196,3197,3200],{"style":714},[572,3198],{"className":3199,"style":698},[697],[572,3201],{"className":3202,"style":722},[721],[572,3204,3205,3208],{"style":972},[572,3206],{"className":3207,"style":698},[697],[572,3209,3211],{"className":3210},[702,703,704,705],[572,3212,3214],{"className":3213},[615,705],[572,3215,882],{"className":3216},[615,705],[572,3218,791],{"className":3219},[790],[572,3221,3223],{"className":3222},[685],[572,3224,3226],{"className":3225,"style":810},[689],[572,3227],{},[572,3229],{"className":3230},[816,673],[572,3232,891],{"className":3233,"style":1020},[615,616],[572,3235,896],{"className":3236},[615,616],{"title":3238,"searchDepth":3239,"depth":3239,"links":3240},"",2,[3241,3242,3243,3244],{"id":560,"depth":3239,"text":561},{"id":855,"depth":3239,"text":856},{"id":1734,"depth":3239,"text":1735},{"id":2716,"depth":3239,"text":2717},[3246,3249,3251,3254,3257,3260,3263],{"lhs":3247,"rhs":3248},"1\u002F2 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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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3271,"x":3272,"y":3275,"items":3278},"Gleichseitiges Dreieck mit der Seitenlänge a und dem Flächeninhalt 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x=\"0\" y=\"0\" width=\"249.6\" height=\"220.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"28.8,187.2 220.8,187.2 124.8,20.93\" class=\"fig-main fig-fill\"\u002F>\u003Ctext x=\"124.8\" y=\"204\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"62.4\" y=\"93.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"187.2\" y=\"93.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"124.8\" y=\"132\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003C\u002Fsvg>","equilateral-triangle-area","A = \\frac{a^2}{4} \\sqrt{3}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmn>4\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmsqrt>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{a^2}{4} \\sqrt{3}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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Sechsecks",{"stem":3340,"title":3341,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fhoehe-gleichseitiges-dreieck","Höhe im gleichseitigen Dreieck",{"stem":3343,"title":3344,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus","Flächeninhalt eines Dreiecks mit Sinus",1793824268465]