document.write( "Question 145155: determin the area of a pentagon of radius 40cm \n" ); document.write( "

Algebra.Com's Answer #105902 by Alan3354(69443) $\"\"$ $\"About$

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Regular polygons are sometimes said to have a radius, defined as the distance from the center to a vertex. This is the same as the radius of a circumscribed circle with the same center. This latter formulation is sometimes used to define the radius of an arbitrary polygon and is called the circumradius.
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\n" ); document.write( "I'll proceed on the assumption that that's what you meant, and also assume that it's a regular pentagon.
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\n" ); document.write( "A regular pentagon can be divided into 5 triangles having 2 angles of 54 degs and one of 72 degs. The 2 sides adjacent to the 72 deg angle are 40 cm long.
\n" ); document.write( "The sides of the pentagon are $\"2%2A40%2Asin%2836%29\"$ and the height of the triangles is $\"40%2Acos%2836%29\"$ . The area is bh/2, which is $\"%2840%2A%282%2A40%2Asin%2836%29%29%2Acos%2836%29%2F2%29\"$ , or $\"1600%2Asin%2836%29%2Acos%2836%29\"$
\n" ); document.write( "This is 800sin(72). As there are 5 of them, the area is 4000sin(72), apx 3804 square cm. \n" ); document.write( "

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