document.write( "Question 556823: what is the maximum number of diagonals can be drawn in a n-sided polygon?
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Algebra.Com's Answer #362248 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "An n-sided polygon has n sides and n vertices.\r\n" );
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document.write( "Every diagonal and every side of the polygon is the line segment \r\n" );
document.write( "connecting a combination of two vertices.  \r\n" );
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document.write( "Every combination of 2 vertices uniquely represents either a side\r\n" );
document.write( "or a diagonal. \r\n" );
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document.write( "Derivation of the formula:\r\n" );
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document.write( "1. First we get the number of sides and diagonals by getting the\r\n" );
document.write( "   number of combinations of n vertices taken 2 at a time:\r\n" );
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document.write( "   C(n,2) =  \r\n" );
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document.write( "2. To get the number of diagonals only, we must subtract the number \r\n" );
document.write( "   of sides, which is n. \r\n" );
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document.write( "    - n\r\n" );
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document.write( "3. We get an LCD of 2 and simplify:\r\n" );
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document.write( "     - \r\n" );
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document.write( "     = \r\n" );
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document.write( "    \r\n" );
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document.write( "So if d represents the number of diagonals of \r\n" );
document.write( "an n-sided polygon, then the formula is\r\n" );
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document.write( "d = \r\n" );
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document.write( "Edwin

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