document.write( "Question 629548: a regular polygon has 170 diagonals and 2.4cm side length. what is its area?
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Algebra.Com's Answer #396385 by AnlytcPhil(1806) $\"\"$ $\"About$

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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" );
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document.write( "     C(n,2) - n = 170 \r\n" );
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document.write( "      - n = 170\r\n" );
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document.write( "     n(n-1) - 2n = 340\r\n" );
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document.write( "     n² - n - 2n - 340 = 0\r\n" );
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document.write( "     n² - 3n - 340 = 0\r\n" );
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document.write( "     (n - 20)(n + 17) = 0\r\n" );
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document.write( "      n = 20,  n = -17\r\n" );
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document.write( "So the regular polygon has 20 sides.\r\n" );
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document.write( "The formula for the area of an n-sided regular polygon is\r\n" );
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document.write( "Area = , where s = lebgth of a side and\r\n" );
document.write( "n = the number of sides.\r\n" );
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document.write( "Area = \r\n" );
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document.write( "Area = \r\n" );
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document.write( "Area = \r\n" );
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document.write( "Area = 181.8360436 cm²\r\n" );
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document.write( "Edwin

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