SOLUTION: determin the area of a pentagon of radius 40cm

Question 145155: determin the area of a pentagon of radius 40cm
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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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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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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.
The sides of the pentagon are and the height of the triangles is . The area is bh/2, which is , or
This is 800sin(72). As there are 5 of them, the area is 4000sin(72), apx 3804 square cm.
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