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\\frac{1}{2} \\cdot a \\cdot \\rho = \\frac{n a^2}{4 \\tan(180^\\circ\u002Fn)}",[573,1133,1135,1154,1174,1256,1274,1292],{"className":1134,"ariaHidden":603},[602],[573,1136,1138,1142,1145,1148,1151],{"className":1137},[607],[573,1139],{"className":1140,"style":1141},[611],"height:0.6833em;",[573,1143,1069],{"className":1144},[616,617],[573,1146],{"className":1147,"style":899},[898],[573,1149,843],{"className":1150},[903],[573,1152],{"className":1153,"style":899},[898],[573,1155,1157,1161,1164,1168,1171],{"className":1156},[607],[573,1158],{"className":1159,"style":1160},[611],"height:0.4445em;",[573,1162,594],{"className":1163},[616,617],[573,1165],{"className":1166,"style":1167},[898],"margin-right:0.2222em;",[573,1169,1076],{"className":1170},[799],[573,1172],{"className":1173,"style":1167},[898],[573,1175,1177,1181,1247,1250,1253],{"className":1176},[607],[573,1178],{"className":1179,"style":1180},[611],"height:2.0074em;vertical-align:-0.686em;",[573,1182,1184,1187,1244],{"className":1183},[616],[573,1185],{"className":1186},[696,697],[573,1188,1190],{"className":1189},[662],[573,1191,1193,1235],{"className":1192},[704,705],[573,1194,1196,1232],{"className":1195},[709],[573,1197,1200,1212,1220],{"className":1198,"style":1199},[713],"height:1.3214em;",[573,1201,1203,1206],{"style":1202},"top:-2.314em;",[573,1204],{"className":1205,"style":722},[721],[573,1207,1209],{"className":1208},[616],[573,1210,852],{"className":1211},[616],[573,1213,1214,1217],{"style":738},[573,1215],{"className":1216,"style":722},[721],[573,1218],{"className":1219,"style":746},[745],[573,1221,1223,1226],{"style":1222},"top:-3.677em;",[573,1224],{"className":1225,"style":722},[721],[573,1227,1229],{"className":1228},[616],[573,1230,1081],{"className":1231},[616],[573,1233,804],{"className":1234},[803],[573,1236,1238],{"className":1237},[709],[573,1239,1242],{"className":1240,"style":1241},[713],"height:0.686em;",[573,1243],{},[573,1245],{"className":1246},[817,697],[573,1248],{"className":1249,"style":1167},[898],[573,1251,1076],{"className":1252},[799],[573,1254],{"className":1255,"style":1167},[898],[573,1257,1259,1262,1265,1268,1271],{"className":1258},[607],[573,1260],{"className":1261,"style":1160},[611],[573,1263,633],{"className":1264},[616,617],[573,1266],{"className":1267,"style":1167},[898],[573,1269,1076],{"className":1270},[799],[573,1272],{"className":1273,"style":1167},[898],[573,1275,1277,1280,1283,1286,1289],{"className":1276},[607],[573,1278],{"className":1279,"style":891},[611],[573,1281,840],{"className":1282},[616,617],[573,1284],{"className":1285,"style":899},[898],[573,1287,843],{"className":1288},[903],[573,1290],{"className":1291,"style":899},[898],[573,1293,1295,1299],{"className":1294},[607],[573,1296],{"className":1297,"style":1298},[611],"height:2.4271em;vertical-align:-0.936em;",[573,1300,1302,1305,1445],{"className":1301},[616],[573,1303],{"className":1304},[696,697],[573,1306,1308],{"className":1307},[662],[573,1309,1311,1436],{"className":1310},[704,705],[573,1312,1314,1433],{"className":1313},[709],[573,1315,1318,1383,1391],{"className":1316,"style":1317},[713],"height:1.4911em;",[573,1319,1320,1323],{"style":1202},[573,1321],{"className":1322,"style":722},[721],[573,1324,1326,1329,1333,1336,1339,1342,1374,1377,1380],{"className":1325},[616],[573,1327,1110],{"className":1328},[616],[573,1330],{"className":1331,"style":1332},[898],"margin-right:0.1667em;",[573,1334,855],{"className":1335},[954],[573,1337,862],{"className":1338},[696],[573,1340,971],{"className":1341},[616],[573,1343,1345,1348],{"className":1344},[616],[573,1346,769],{"className":1347},[616],[573,1349,1351],{"className":1350},[773],[573,1352,1354],{"className":1353},[704],[573,1355,1357],{"className":1356},[709],[573,1358,1361],{"className":1359,"style":1360},[713],"height:0.6001em;",[573,1362,1364,1368],{"style":1363},"top:-2.989em;margin-right:0.05em;",[573,1365],{"className":1366,"style":1367},[721],"height:2.7em;",[573,1369,1371],{"className":1370},[726,727,728,729],[573,1372,674],{"className":1373},[799,729],[573,1375,873],{"className":1376},[616],[573,1378,594],{"className":1379},[616,617],[573,1381,878],{"className":1382},[817],[573,1384,1385,1388],{"style":738},[573,1386],{"className":1387,"style":722},[721],[573,1389],{"className":1390,"style":746},[745],[573,1392,1393,1396],{"style":1222},[573,1394],{"className":1395,"style":722},[721],[573,1397,1399,1402],{"className":1398},[616],[573,1400,594],{"className":1401},[616,617],[573,1403,1405,1408],{"className":1404},[616],[573,1406,633],{"className":1407},[616,617],[573,1409,1411],{"className":1410},[773],[573,1412,1414],{"className":1413},[704],[573,1415,1417],{"className":1416},[709],[573,1418,1421],{"className":1419,"style":1420},[713],"height:0.8141em;",[573,1422,1424,1427],{"style":1423},"top:-3.063em;margin-right:0.05em;",[573,1425],{"className":1426,"style":1367},[721],[573,1428,1430],{"className":1429},[726,727,728,729],[573,1431,852],{"className":1432},[616,729],[573,1434,804],{"className":1435},[803],[573,1437,1439],{"className":1438},[709],[573,1440,1443],{"className":1441,"style":1442},[713],"height:0.936em;",[573,1444],{},[573,1446],{"className":1447},[817,697],[564,1449,1450,1451,825,1454,1484],{},"Kennt man statt der Seite den ",[568,1452,1453],{},"Umkreisradius",[573,1455,1457,1471],{"className":1456},[576],[573,1458,1460],{"className":1459},[580],[582,1461,1462],{"xmlns":584},[586,1463,1464,1469],{},[589,1465,1466],{},[592,1467,1468],{},"r",[596,1470,1468],{"encoding":598},[573,1472,1474],{"className":1473,"ariaHidden":603},[602],[573,1475,1477,1480],{"className":1476},[607],[573,1478],{"className":1479,"style":612},[611],[573,1481,1468],{"className":1482,"style":1483},[616,617],"margin-right:0.0278em;",", gilt",[573,1486,1488],{"className":1487},[1053],[573,1489,1491,1544],{"className":1490},[576],[573,1492,1494],{"className":1493},[580],[582,1495,1496],{"xmlns":584,"display":1062},[586,1497,1498,1541],{},[589,1499,1500,1502,1504,1510,1514,1520,1523,1525],{},[592,1501,1069],{},[672,1503,843],{},[662,1505,1506,1508],{},[592,1507,594],{},[668,1509,852],{},[1511,1512,1513],"mtext",{}," ",[665,1515,1516,1518],{},[592,1517,1468],{},[668,1519,852],{},[592,1521,1522],{},"sin",[672,1524,858],{},[589,1526,1527,1529,1539],{},[672,1528,862],{"fence":603},[662,1530,1531,1537],{},[665,1532,1533,1535],{},[668,1534,670],{},[672,1536,674],{},[592,1538,594],{},[672,1540,878],{"fence":603},[596,1542,1543],{"encoding":598},"A = \\frac{n}{2} \\, r^2 \\sin\\left(\\frac{360^\\circ}{n}\\right)",[573,1545,1547,1565],{"className":1546,"ariaHidden":603},[602],[573,1548,1550,1553,1556,1559,1562],{"className":1549},[607],[573,1551],{"className":1552,"style":1141},[611],[573,1554,1069],{"className":1555},[616,617],[573,1557],{"className":1558,"style":899},[898],[573,1560,843],{"className":1561},[903],[573,1563],{"className":1564,"style":899},[898],[573,1566,1568,1572,1635,1638,1669,1672,1675,1678],{"className":1567},[607],[573,1569],{"className":1570,"style":1571},[611],"height:2.4em;vertical-align:-0.95em;",[573,1573,1575,1578,1632],{"className":1574},[616],[573,1576],{"className":1577},[696,697],[573,1579,1581],{"className":1580},[662],[573,1582,1584,1624],{"className":1583},[704,705],[573,1585,1587,1621],{"className":1586},[709],[573,1588,1591,1602,1610],{"className":1589,"style":1590},[713],"height:1.1076em;",[573,1592,1593,1596],{"style":1202},[573,1594],{"className":1595,"style":722},[721],[573,1597,1599],{"className":1598},[616],[573,1600,852],{"className":1601},[616],[573,1603,1604,1607],{"style":738},[573,1605],{"className":1606,"style":722},[721],[573,1608],{"className":1609,"style":746},[745],[573,1611,1612,1615],{"style":1222},[573,1613],{"className":1614,"style":722},[721],[573,1616,1618],{"className":1617},[616],[573,1619,594],{"className":1620},[616,617],[573,1622,804],{"className":1623},[803],[573,1625,1627],{"className":1626},[709],[573,1628,1630],{"className":1629,"style":1241},[713],[573,1631],{},[573,1633],{"className":1634},[817,697],[573,1636],{"className":1637,"style":1332},[898],[573,1639,1641,1644],{"className":1640},[616],[573,1642,1468],{"className":1643,"style":1483},[616,617],[573,1645,1647],{"className":1646},[773],[573,1648,1650],{"className":1649},[704],[573,1651,1653],{"className":1652},[709],[573,1654,1657],{"className":1655,"style":1656},[713],"height:0.8641em;",[573,1658,1660,1663],{"style":1659},"top:-3.113em;margin-right:0.05em;",[573,1661],{"className":1662,"style":1367},[721],[573,1664,1666],{"className":1665},[726,727,728,729],[573,1667,852],{"className":1668},[616,729],[573,1670],{"className":1671,"style":1332},[898],[573,1673,1522],{"className":1674},[954],[573,1676],{"className":1677,"style":1332},[898],[573,1679,1682,1691,1784],{"className":1680},[1681],"minner",[573,1683,1687],{"className":1684,"style":1686},[696,1685],"delimcenter","top:0em;",[573,1688,862],{"className":1689},[1690,728],"delimsizing",[573,1692,1694,1697,1781],{"className":1693},[616],[573,1695],{"className":1696},[696,697],[573,1698,1700],{"className":1699},[662],[573,1701,1703,1773],{"className":1702},[704,705],[573,1704,1706,1770],{"className":1705},[709],[573,1707,1710,1721,1729],{"className":1708,"style":1709},[713],"height:1.3511em;",[573,1711,1712,1715],{"style":1202},[573,1713],{"className":1714,"style":722},[721],[573,1716,1718],{"className":1717},[616],[573,1719,594],{"className":1720},[616,617],[573,1722,1723,1726],{"style":738},[573,1724],{"className":1725,"style":722},[721],[573,1727],{"className":1728,"style":746},[745],[573,1730,1731,1734],{"style":1222},[573,1732],{"className":1733,"style":722},[721],[573,1735,1737,1740],{"className":1736},[616],[573,1738,762],{"className":1739},[616],[573,1741,1743,1746],{"className":1742},[616],[573,1744,769],{"className":1745},[616],[573,1747,1749],{"className":1748},[773],[573,1750,1752],{"className":1751},[704],[573,1753,1755],{"className":1754},[709],[573,1756,1759],{"className":1757,"style":1758},[713],"height:0.6741em;",[573,1760,1761,1764],{"style":1423},[573,1762],{"className":1763,"style":1367},[721],[573,1765,1767],{"className":1766},[726,727,728,729],[573,1768,674],{"className":1769},[799,729],[573,1771,804],{"className":1772},[803],[573,1774,1776],{"className":1775},[709],[573,1777,1779],{"className":1778,"style":1241},[713],[573,1780],{},[573,1782],{"className":1783},[817,697],[573,1785,1787],{"className":1786,"style":1686},[817,1685],[573,1788,878],{"className":1789},[1690,728],[564,1791,1792,1793,1846,1847,1875,1876,1905],{},"Für ",[573,1794,1796,1815],{"className":1795},[576],[573,1797,1799],{"className":1798},[580],[582,1800,1801],{"xmlns":584},[586,1802,1803,1812],{},[589,1804,1805,1807,1809],{},[592,1806,594],{},[672,1808,843],{},[668,1810,1811],{},"3",[596,1813,1814],{"encoding":598},"n = 3",[573,1816,1818,1836],{"className":1817,"ariaHidden":603},[602],[573,1819,1821,1824,1827,1830,1833],{"className":1820},[607],[573,1822],{"className":1823,"style":612},[611],[573,1825,594],{"className":1826},[616,617],[573,1828],{"className":1829,"style":899},[898],[573,1831,843],{"className":1832},[903],[573,1834],{"className":1835,"style":899},[898],[573,1837,1839,1843],{"className":1838},[607],[573,1840],{"className":1841,"style":1842},[611],"height:0.6444em;",[573,1844,1811],{"className":1845},[616],", ",[573,1848,1850,1863],{"className":1849},[576],[573,1851,1853],{"className":1852},[580],[582,1854,1855],{"xmlns":584},[586,1856,1857,1861],{},[589,1858,1859],{},[668,1860,1110],{},[596,1862,1110],{"encoding":598},[573,1864,1866],{"className":1865,"ariaHidden":603},[602],[573,1867,1869,1872],{"className":1868},[607],[573,1870],{"className":1871,"style":1842},[611],[573,1873,1110],{"className":1874},[616]," und ",[573,1877,1879,1893],{"className":1878},[576],[573,1880,1882],{"className":1881},[580],[582,1883,1884],{"xmlns":584},[586,1885,1886,1891],{},[589,1887,1888],{},[668,1889,1890],{},"6",[596,1892,1890],{"encoding":598},[573,1894,1896],{"className":1895,"ariaHidden":603},[602],[573,1897,1899,1902],{"className":1898},[607],[573,1900],{"className":1901,"style":1842},[611],[573,1903,1890],{"className":1904},[616]," ergeben sich die bekannten Formeln für das gleichseitige Dreieck, das Quadrat und das regelmäßige Sechseck.",[559,1907,1909],{"id":1908},"beispiele","Beispiele",[564,1911,1912,1913,1979],{},"Regelmäßiges Fünfeck mit ",[573,1914,1916,1939],{"className":1915},[576],[573,1917,1919],{"className":1918},[580],[582,1920,1921],{"xmlns":584},[586,1922,1923,1936],{},[589,1924,1925,1927,1929,1931,1933],{},[592,1926,633],{},[672,1928,843],{},[668,1930,1110],{},[1511,1932,1513],{},[1511,1934,1935],{},"cm",[596,1937,1938],{"encoding":598},"a = 4\\,\\text{cm}",[573,1940,1942,1960],{"className":1941,"ariaHidden":603},[602],[573,1943,1945,1948,1951,1954,1957],{"className":1944},[607],[573,1946],{"className":1947,"style":612},[611],[573,1949,633],{"className":1950},[616,617],[573,1952],{"className":1953,"style":899},[898],[573,1955,843],{"className":1956},[903],[573,1958],{"className":1959,"style":899},[898],[573,1961,1963,1966,1969,1972],{"className":1962},[607],[573,1964],{"className":1965,"style":1842},[611],[573,1967,1110],{"className":1968},[616],[573,1970],{"className":1971,"style":1332},[898],[573,1973,1976],{"className":1974},[616,1975],"text",[573,1977,1935],{"className":1978},[616],":",[573,1981,1983],{"className":1982},[1053],[573,1984,1986,2061],{"className":1985},[576],[573,1987,1989],{"className":1988},[580],[582,1990,1991],{"xmlns":584,"display":1062},[586,1992,1993,2058],{},[589,1994,1995,1997,1999,2025,2027,2044,2047,2050,2052],{},[592,1996,1069],{},[672,1998,843],{},[662,2000,2001,2011],{},[589,2002,2003,2006,2008],{},[668,2004,2005],{},"5",[672,2007,1076],{},[668,2009,2010],{},"16",[589,2012,2013,2015,2017,2019],{},[668,2014,1110],{},[592,2016,855],{},[672,2018,858],{},[665,2020,2021,2023],{},[668,2022,762],{},[672,2024,674],{},[672,2026,843],{},[662,2028,2029,2032],{},[668,2030,2031],{},"20",[589,2033,2034,2036,2038],{},[592,2035,855],{},[672,2037,858],{},[665,2039,2040,2042],{},[668,2041,762],{},[672,2043,674],{},[672,2045,2046],{},"≈",[668,2048,2049],{},"27,53",[1511,2051,1513],{},[665,2053,2054,2056],{},[1511,2055,1935],{},[668,2057,852],{},[596,2059,2060],{"encoding":598},"A = \\frac{5 \\cdot 16}{4 \\tan 36^\\circ} = \\frac{20}{\\tan 36^\\circ} \\approx 27{,}53\\,\\text{cm}^2",[573,2062,2064,2082,2212,2324],{"className":2063,"ariaHidden":603},[602],[573,2065,2067,2070,2073,2076,2079],{"className":2066},[607],[573,2068],{"className":2069,"style":1141},[611],[573,2071,1069],{"className":2072},[616,617],[573,2074],{"className":2075,"style":899},[898],[573,2077,843],{"className":2078},[903],[573,2080],{"className":2081,"style":899},[898],[573,2083,2085,2088,2203,2206,2209],{"className":2084},[607],[573,2086],{"className":2087,"style":1180},[611],[573,2089,2091,2094,2200],{"className":2090},[616],[573,2092],{"className":2093},[696,697],[573,2095,2097],{"className":2096},[662],[573,2098,2100,2192],{"className":2099},[704,705],[573,2101,2103,2189],{"className":2102},[709],[573,2104,2106,2158,2166],{"className":2105,"style":1199},[713],[573,2107,2108,2111],{"style":1202},[573,2109],{"className":2110,"style":722},[721],[573,2112,2114,2117,2120,2123,2126,2129],{"className":2113},[616],[573,2115,1110],{"className":2116},[616],[573,2118],{"className":2119,"style":1332},[898],[573,2121,855],{"className":2122},[954],[573,2124],{"className":2125,"style":1332},[898],[573,2127,1811],{"className":2128},[616],[573,2130,2132,2135],{"className":2131},[616],[573,2133,1890],{"className":2134},[616],[573,2136,2138],{"className":2137},[773],[573,2139,2141],{"className":2140},[704],[573,2142,2144],{"className":2143},[709],[573,2145,2147],{"className":2146,"style":1360},[713],[573,2148,2149,2152],{"style":1363},[573,2150],{"className":2151,"style":1367},[721],[573,2153,2155],{"className":2154},[726,727,728,729],[573,2156,674],{"className":2157},[799,729],[573,2159,2160,2163],{"style":738},[573,2161],{"className":2162,"style":722},[721],[573,2164],{"className":2165,"style":746},[745],[573,2167,2168,2171],{"style":1222},[573,2169],{"className":2170,"style":722},[721],[573,2172,2174,2177,2180,2183,2186],{"className":2173},[616],[573,2175,2005],{"className":2176},[616],[573,2178],{"className":2179,"style":1167},[898],[573,2181,1076],{"className":2182},[799],[573,2184],{"className":2185,"style":1167},[898],[573,2187,2010],{"className":2188},[616],[573,2190,804],{"className":2191},[803],[573,2193,2195],{"className":2194},[709],[573,2196,2198],{"className":2197,"style":1241},[713],[573,2199],{},[573,2201],{"className":2202},[817,697],[573,2204],{"className":2205,"style":899},[898],[573,2207,843],{"className":2208},[903],[573,2210],{"className":2211,"style":899},[898],[573,2213,2215,2218,2315,2318,2321],{"className":2214},[607],[573,2216],{"className":2217,"style":1180},[611],[573,2219,2221,2224,2312],{"className":2220},[616],[573,2222],{"className":2223},[696,697],[573,2225,2227],{"className":2226},[662],[573,2228,2230,2304],{"className":2229},[704,705],[573,2231,2233,2301],{"className":2232},[709],[573,2234,2236,2282,2290],{"className":2235,"style":1199},[713],[573,2237,2238,2241],{"style":1202},[573,2239],{"className":2240,"style":722},[721],[573,2242,2244,2247,2250,2253],{"className":2243},[616],[573,2245,855],{"className":2246},[954],[573,2248],{"className":2249,"style":1332},[898],[573,2251,1811],{"className":2252},[616],[573,2254,2256,2259],{"className":2255},[616],[573,2257,1890],{"className":2258},[616],[573,2260,2262],{"className":2261},[773],[573,2263,2265],{"className":2264},[704],[573,2266,2268],{"className":2267},[709],[573,2269,2271],{"className":2270,"style":1360},[713],[573,2272,2273,2276],{"style":1363},[573,2274],{"className":2275,"style":1367},[721],[573,2277,2279],{"className":2278},[726,727,728,729],[573,2280,674],{"className":2281},[799,729],[573,2283,2284,2287],{"style":738},[573,2285],{"className":2286,"style":722},[721],[573,2288],{"className":2289,"style":746},[745],[573,2291,2292,2295],{"style":1222},[573,2293],{"className":2294,"style":722},[721],[573,2296,2298],{"className":2297},[616],[573,2299,2031],{"className":2300},[616],[573,2302,804],{"className":2303},[803],[573,2305,2307],{"className":2306},[709],[573,2308,2310],{"className":2309,"style":1241},[713],[573,2311],{},[573,2313],{"className":2314},[817,697],[573,2316],{"className":2317,"style":899},[898],[573,2319,2046],{"className":2320},[903],[573,2322],{"className":2323,"style":899},[898],[573,2325,2327,2331,2335,2343,2347,2350],{"className":2326},[607],[573,2328],{"className":2329,"style":2330},[611],"height:1.0585em;vertical-align:-0.1944em;",[573,2332,2334],{"className":2333},[616],"27",[573,2336,2338],{"className":2337},[616],[573,2339,2342],{"className":2340},[2341],"mpunct",",",[573,2344,2346],{"className":2345},[616],"53",[573,2348],{"className":2349,"style":1332},[898],[573,2351,2353,2359],{"className":2352},[616],[573,2354,2356],{"className":2355},[616,1975],[573,2357,1935],{"className":2358},[616],[573,2360,2362],{"className":2361},[773],[573,2363,2365],{"className":2364},[704],[573,2366,2368],{"className":2367},[709],[573,2369,2371],{"className":2370,"style":1656},[713],[573,2372,2373,2376],{"style":1659},[573,2374],{"className":2375,"style":1367},[721],[573,2377,2379],{"className":2378},[726,727,728,729],[573,2380,852],{"className":2381},[616,729],[564,2383,2384,2385,1979],{},"Regelmäßiges Achteck mit ",[573,2386,2388,2410],{"className":2387},[576],[573,2389,2391],{"className":2390},[580],[582,2392,2393],{"xmlns":584},[586,2394,2395,2407],{},[589,2396,2397,2399,2401,2403,2405],{},[592,2398,633],{},[672,2400,843],{},[668,2402,852],{},[1511,2404,1513],{},[1511,2406,1935],{},[596,2408,2409],{"encoding":598},"a = 2\\,\\text{cm}",[573,2411,2413,2431],{"className":2412,"ariaHidden":603},[602],[573,2414,2416,2419,2422,2425,2428],{"className":2415},[607],[573,2417],{"className":2418,"style":612},[611],[573,2420,633],{"className":2421},[616,617],[573,2423],{"className":2424,"style":899},[898],[573,2426,843],{"className":2427},[903],[573,2429],{"className":2430,"style":899},[898],[573,2432,2434,2437,2440,2443],{"className":2433},[607],[573,2435],{"className":2436,"style":1842},[611],[573,2438,852],{"className":2439},[616],[573,2441],{"className":2442,"style":1332},[898],[573,2444,2446],{"className":2445},[616,1975],[573,2447,1935],{"className":2448},[616],[573,2450,2452],{"className":2451},[1053],[573,2453,2455,2530],{"className":2454},[576],[573,2456,2458],{"className":2457},[580],[582,2459,2460],{"xmlns":584,"display":1062},[586,2461,2462,2527],{},[589,2463,2464,2466,2468,2494,2496,2498,2514,2516,2519,2521],{},[592,2465,1069],{},[672,2467,843],{},[662,2469,2470,2479],{},[589,2471,2472,2475,2477],{},[668,2473,2474],{},"8",[672,2476,1076],{},[668,2478,1110],{},[589,2480,2481,2483,2485,2487],{},[668,2482,1110],{},[592,2484,855],{},[672,2486,858],{},[665,2488,2489,2492],{},[668,2490,2491],{},"22,5",[672,2493,674],{},[672,2495,843],{},[668,2497,2474],{},[589,2499,2500,2502,2504,2507,2512],{},[672,2501,862],{"fence":603},[668,2503,1081],{},[672,2505,2506],{},"+",[2508,2509,2510],"msqrt",{},[668,2511,852],{},[672,2513,878],{"fence":603},[672,2515,2046],{},[668,2517,2518],{},"19,31",[1511,2520,1513],{},[665,2522,2523,2525],{},[1511,2524,1935],{},[668,2526,852],{},[596,2528,2529],{"encoding":598},"A = \\frac{8 \\cdot 4}{4 \\tan 22{,}5^\\circ} = 8\\left(1 + \\sqrt{2}\\right) \\approx 19{,}31\\,\\text{cm}^2",[573,2531,2533,2551,2690,2804],{"className":2532,"ariaHidden":603},[602],[573,2534,2536,2539,2542,2545,2548],{"className":2535},[607],[573,2537],{"className":2538,"style":1141},[611],[573,2540,1069],{"className":2541},[616,617],[573,2543],{"className":2544,"style":899},[898],[573,2546,843],{"className":2547},[903],[573,2549],{"className":2550,"style":899},[898],[573,2552,2554,2558,2681,2684,2687],{"className":2553},[607],[573,2555],{"className":2556,"style":2557},[611],"height:2.2019em;vertical-align:-0.8804em;",[573,2559,2561,2564,2678],{"className":2560},[616],[573,2562],{"className":2563},[696,697],[573,2565,2567],{"className":2566},[662],[573,2568,2570,2669],{"className":2569},[704,705],[573,2571,2573,2666],{"className":2572},[709],[573,2574,2576,2635,2643],{"className":2575,"style":1199},[713],[573,2577,2578,2581],{"style":1202},[573,2579],{"className":2580,"style":722},[721],[573,2582,2584,2587,2590,2593,2596,2600,2606],{"className":2583},[616],[573,2585,1110],{"className":2586},[616],[573,2588],{"className":2589,"style":1332},[898],[573,2591,855],{"className":2592},[954],[573,2594],{"className":2595,"style":1332},[898],[573,2597,2599],{"className":2598},[616],"22",[573,2601,2603],{"className":2602},[616],[573,2604,2342],{"className":2605},[2341],[573,2607,2609,2612],{"className":2608},[616],[573,2610,2005],{"className":2611},[616],[573,2613,2615],{"className":2614},[773],[573,2616,2618],{"className":2617},[704],[573,2619,2621],{"className":2620},[709],[573,2622,2624],{"className":2623,"style":1360},[713],[573,2625,2626,2629],{"style":1363},[573,2627],{"className":2628,"style":1367},[721],[573,2630,2632],{"className":2631},[726,727,728,729],[573,2633,674],{"className":2634},[799,729],[573,2636,2637,2640],{"style":738},[573,2638],{"className":2639,"style":722},[721],[573,2641],{"className":2642,"style":746},[745],[573,2644,2645,2648],{"style":1222},[573,2646],{"className":2647,"style":722},[721],[573,2649,2651,2654,2657,2660,2663],{"className":2650},[616],[573,2652,2474],{"className":2653},[616],[573,2655],{"className":2656,"style":1167},[898],[573,2658,1076],{"className":2659},[799],[573,2661],{"className":2662,"style":1167},[898],[573,2664,1110],{"className":2665},[616],[573,2667,804],{"className":2668},[803],[573,2670,2672],{"className":2671},[709],[573,2673,2676],{"className":2674,"style":2675},[713],"height:0.8804em;",[573,2677],{},[573,2679],{"className":2680},[817,697],[573,2682],{"className":2683,"style":899},[898],[573,2685,843],{"className":2686},[903],[573,2688],{"className":2689,"style":899},[898],[573,2691,2693,2697,2700,2703,2795,2798,2801],{"className":2692},[607],[573,2694],{"className":2695,"style":2696},[611],"height:1.8em;vertical-align:-0.65em;",[573,2698,2474],{"className":2699},[616],[573,2701],{"className":2702,"style":1332},[898],[573,2704,2706,2713,2716,2719,2722,2725,2789],{"className":2705},[1681],[573,2707,2709],{"className":2708,"style":1686},[696,1685],[573,2710,862],{"className":2711},[1690,2712],"size2",[573,2714,1081],{"className":2715},[616],[573,2717],{"className":2718,"style":1167},[898],[573,2720,2506],{"className":2721},[799],[573,2723],{"className":2724,"style":1167},[898],[573,2726,2729],{"className":2727},[616,2728],"sqrt",[573,2730,2732,2780],{"className":2731},[704,705],[573,2733,2735,2777],{"className":2734},[709],[573,2736,2739,2754],{"className":2737,"style":2738},[713],"height:0.9561em;",[573,2740,2744,2747],{"className":2741,"style":2743},[2742],"svg-align","top:-3em;",[573,2745],{"className":2746,"style":722},[721],[573,2748,2751],{"className":2749,"style":2750},[616],"padding-left:0.833em;",[573,2752,852],{"className":2753},[616],[573,2755,2757,2760],{"style":2756},"top:-2.9161em;",[573,2758],{"className":2759,"style":722},[721],[573,2761,2765],{"className":2762,"style":2764},[2763],"hide-tail","min-width:0.853em;height:1.08em;",[2766,2767,2773],"svg",{"xmlns":2768,"width":2769,"height":2770,"viewBox":2771,"preserveAspectRatio":2772},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2774,2775],"path",{"d":2776},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[573,2778,804],{"className":2779},[803],[573,2781,2783],{"className":2782},[709],[573,2784,2787],{"className":2785,"style":2786},[713],"height:0.0839em;",[573,2788],{},[573,2790,2792],{"className":2791,"style":1686},[817,1685],[573,2793,878],{"className":2794},[1690,2712],[573,2796],{"className":2797,"style":899},[898],[573,2799,2046],{"className":2800},[903],[573,2802],{"className":2803,"style":899},[898],[573,2805,2807,2810,2814,2820,2824,2827],{"className":2806},[607],[573,2808],{"className":2809,"style":2330},[611],[573,2811,2813],{"className":2812},[616],"19",[573,2815,2817],{"className":2816},[616],[573,2818,2342],{"className":2819},[2341],[573,2821,2823],{"className":2822},[616],"31",[573,2825],{"className":2826,"style":1332},[898],[573,2828,2830,2836],{"className":2829},[616],[573,2831,2833],{"className":2832},[616,1975],[573,2834,1935],{"className":2835},[616],[573,2837,2839],{"className":2838},[773],[573,2840,2842],{"className":2841},[704],[573,2843,2845],{"className":2844},[709],[573,2846,2848],{"className":2847,"style":1656},[713],[573,2849,2850,2853],{"style":1659},[573,2851],{"className":2852,"style":1367},[721],[573,2854,2856],{"className":2855},[726,727,728,729],[573,2857,852],{"className":2858},[616,729],[559,2860,2862],{"id":2861},"typische-fehler","Typische Fehler",[2864,2865,2866,3021,3024],"ul",{},[2867,2868,2869,2870,2943,2944,3016,3017,3020],"li",{},"Im Tangens ",[573,2871,2873,2895],{"className":2872},[576],[573,2874,2876],{"className":2875},[580],[582,2877,2878],{"xmlns":584},[586,2879,2880,2892],{},[589,2881,2882,2888,2890],{},[665,2883,2884,2886],{},[668,2885,670],{},[672,2887,674],{},[592,2889,873],{"mathvariant":872},[592,2891,594],{},[596,2893,2894],{"encoding":598},"360^\\circ\u002Fn",[573,2896,2898],{"className":2897,"ariaHidden":603},[602],[573,2899,2901,2905,2908,2937,2940],{"className":2900},[607],[573,2902],{"className":2903,"style":2904},[611],"height:1em;vertical-align:-0.25em;",[573,2906,762],{"className":2907},[616],[573,2909,2911,2914],{"className":2910},[616],[573,2912,769],{"className":2913},[616],[573,2915,2917],{"className":2916},[773],[573,2918,2920],{"className":2919},[704],[573,2921,2923],{"className":2922},[709],[573,2924,2926],{"className":2925,"style":1758},[713],[573,2927,2928,2931],{"style":1423},[573,2929],{"className":2930,"style":1367},[721],[573,2932,2934],{"className":2933},[726,727,728,729],[573,2935,674],{"className":2936},[799,729],[573,2938,873],{"className":2939},[616],[573,2941,594],{"className":2942},[616,617]," statt ",[573,2945,2947,2969],{"className":2946},[576],[573,2948,2950],{"className":2949},[580],[582,2951,2952],{"xmlns":584},[586,2953,2954,2966],{},[589,2955,2956,2962,2964],{},[665,2957,2958,2960],{},[668,2959,867],{},[672,2961,674],{},[592,2963,873],{"mathvariant":872},[592,2965,594],{},[596,2967,2968],{"encoding":598},"180^\\circ\u002Fn",[573,2970,2972],{"className":2971,"ariaHidden":603},[602],[573,2973,2975,2978,2981,3010,3013],{"className":2974},[607],[573,2976],{"className":2977,"style":2904},[611],[573,2979,971],{"className":2980},[616],[573,2982,2984,2987],{"className":2983},[616],[573,2985,769],{"className":2986},[616],[573,2988,2990],{"className":2989},[773],[573,2991,2993],{"className":2992},[704],[573,2994,2996],{"className":2995},[709],[573,2997,2999],{"className":2998,"style":1758},[713],[573,3000,3001,3004],{"style":1423},[573,3002],{"className":3003,"style":1367},[721],[573,3005,3007],{"className":3006},[726,727,728,729],[573,3008,674],{"className":3009},[799,729],[573,3011,873],{"className":3012},[616],[573,3014,594],{"className":3015},[616,617]," einsetzen. Der Tangens gehört zum ",[568,3018,3019],{},"halben"," Mittelpunktswinkel.",[2867,3022,3023],{},"Den Taschenrechner im Bogenmaß-Modus haben, während man Gradwinkel eintippt.",[2867,3025,3026],{},"Die Formel auf unregelmäßige Vielecke anwenden. Sie gilt nur, wenn alle Seiten und Winkel gleich sind.",{"title":3028,"searchDepth":3029,"depth":3029,"links":3030},"",2,[3031,3032,3033],{"id":561,"depth":3029,"text":562},{"id":1908,"depth":3029,"text":1909},{"id":2861,"depth":3029,"text":2862},[3035,3040,3044,3048,3052,3055,3058,3061],{"lhs":3036,"rhs":3037,"where":3038},"n*a^2\u002F(4*tan(pi\u002Fn))","sqrt(3)\u002F4*a^2",{"n":3039},3,{"lhs":3036,"rhs":3041,"where":3042},"a^2",{"n":3043},4,{"lhs":3036,"rhs":3045,"where":3046},"3\u002F2*a^2*sqrt(3)",{"n":3047},6,{"lhs":3049,"rhs":3036,"where":3050},"n\u002F2*(a\u002F(2*sin(pi\u002Fn)))^2*sin(2*pi\u002Fn)",{"n":3051},5,{"lhs":3053,"rhs":3054},"5*4^2\u002F(4*tan(36*pi\u002F180))","20\u002Ftan(36*pi\u002F180)",{"lhs":3056,"rhs":3057},"round(20\u002Ftan(36*pi\u002F180), 2)","27.53",{"lhs":3059,"rhs":3060},"8*2^2\u002F(4*tan(22.5*pi\u002F180))","8*(1 + sqrt(2))",{"lhs":3062,"rhs":3063},"round(8*(1 + sqrt(2)), 2)","19.31","n \\ge 3","\u003Cspan class=\"katex\">\u003Cspan 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