document.write( "Question 793226: a regular pentagon I inscribed in a circle whose radius is 9 in. find the area of the pentagon \n" ); document.write( "

Algebra.Com's Answer #480297 by KMST(5328) $\"\"$ $\"About$

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Here is your pentagon (in red), with the circle, and the radii to the pentagon vertices (in green).
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Those radii split the pentagon into 5 congruent isosceles triangles.
\n" ); document.write( "The area of a triangle can be calculated as $\"a%2Ab%2Asin%28C%29\"$ if you know the measures of sides $\"a\"$ and $\"b\"$ and angle $\"C\"$ between those two sides.
\n" ); document.write( "In this case, two of the sides are the radii, measuring $\"9in\"$ , and the angle between them measures $\"72%5Eo\"$ .
\n" ); document.write( "The area of one of those triangles is
\n" ); document.write( " $\"%289in%29%2A%289in%29%2Asin%2872%5Eo%29\"$ = approx. $\"81%2A0.951\"$ $\"in%5E2\"$ = $\"77in%5E2\"$
\n" ); document.write( "The area of the pentagon is approximately $\"5%2A77in%5E2=385in%5E2\"$ \n" ); document.write( "

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