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
