document.write( "Question 630017: The number of diagonals of a regular polygon is 35. Find the area of the polygon if its apothem measures 10 cm. \n" ); document.write( "
Algebra.Com's Answer #396634 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "There are n vertices, there are C(n,2) ways to connect 2 of them.\r\n" );
document.write( "All of these represent diagonals except the n sides, so the number\r\n" );
document.write( "of diagonals is\r\n" );
document.write( "\r\n" );
document.write( "     C(n,2) - n = 35 \r\n" );
document.write( "\r\n" );
document.write( "     \"%28n%28n-1%29%29%2F2\" - n = 35\r\n" );
document.write( "     \r\n" );
document.write( "     n(n-1) - 2n = 70\r\n" );
document.write( "\r\n" );
document.write( "     nē - n - 2n - 70 = 0\r\n" );
document.write( "\r\n" );
document.write( "     nē - 3n - 70 = 0\r\n" );
document.write( "   \r\n" );
document.write( "     (n - 10)(n + 7) = 0\r\n" );
document.write( "\r\n" );
document.write( "      n = 10,  n = -7, which we discard.\r\n" );
document.write( "\r\n" );
document.write( "So the regular polygon has 10 sides.\r\n" );
document.write( "\r\n" );
document.write( "The formula for the area of an n-sided regular polygon is\r\n" );
document.write( "\r\n" );
document.write( "Area = \"na%5E2tan%28%22180%B0%22%2Fn%29\", where a = apothem and \r\n" );
document.write( "n = the number of sides.\r\n" );
document.write( "\r\n" );
document.write( "Area = \"10%2A10%5E2tan%28%22180%B0%22%2F10%29\"\r\n" );
document.write( "\r\n" );
document.write( "Area = \"%2810%2A100%2Atan%28%2218%B0%22%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Area = \"%281000%29%2Atan%28%2218%B0%22%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Area = 324.9196962 square units of area\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "
\n" );