document.write( "Question 1066704: The area of a convex regular polygon is 192√3 cm2. The polygon has nine diagonals. Find the perimeter of the polygon, in centimeters \n" ); document.write( "

Algebra.Com's Answer #681924 by Fombitz(32388) $\"\"$ $\"About$

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The number of sides of a polygon using the number of diagonals is,
\n" ); document.write( " $\"D=S%28S-3%29%2F2\"$
\n" ); document.write( " $\"9=S%28S-3%29%2F2\"$
\n" ); document.write( " $\"S%5E2-3S=18\"$
\n" ); document.write( " $\"S%5E2-3S-18=0\"$
\n" ); document.write( " $\"%28S-6%29%28S%2B3%29=0\"$
\n" ); document.write( " $\"S-6=0\"$
\n" ); document.write( " $\"S=6\"$
\n" ); document.write( "So it's a hexagon.\r
\n" ); document.write( "\n" ); document.write( " $\"A%5BHEX%5D=+%283%2F2%29sqrt%283%29X%5E2\"$
\n" ); document.write( " $\"%283%2F2%29sqrt%283%29X%5E2=196sqrt%283%29\"$
\n" ); document.write( " $\"X%5E2=392%2F3\"$
\n" ); document.write( " $\"X=sqrt%28392%2F3%29\"$
\n" ); document.write( " $\"X=%2814%2F3%29sqrt%286%29\"$
\n" ); document.write( "So the perimeter is then,
\n" ); document.write( " $\"P=6X\"$
\n" ); document.write( " $\"P=28sqrt%286%29\"$ $\"cm\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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