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

Sagot :

CamilleEaton210idn
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

Answer:

Step-by-step explanation:

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