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13 October, 22:20

A regular pentagon is inscribed in a circle whose radius measures 9 inches. Find the area of the pentagon.

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  1. 14 October, 01:53
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    Since the Pentagon can be divided into 5 equal triangles, and each of the angle opposite the sides of the pentagon is 360/5 = 72 degree.

    Also, since each of the 5 triangles from the divided pentagon is an isoceles triangle (same 2 sides = radius), the 2 base angles are equal. Base angle = (180 - 72) / 2 = 54.

    Using Sine Law to calculate side of the Pentagon:

    Side/sin (72) = radius / sin (54) = 9/sin (54)

    Side = 10.58

    Therefore each triangle has an area of:

    = 0.5 (side) (radius) sin (54) = 0.5 (10.58) (9) sin (54)

    = 38.52

    Total area of Pentagon = 5 x 38.52 = 192.60
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