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

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