A regular pentagon is inscribed in a circle with a radius of 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

Answered by CamilleEaton210 | 2024-06-10

Answered by cristygardea3 | 2024-06-14

The area of a regular pentagon inscribed in a circle with a radius of 9 inches is approximately 192.60 square inches. This is found by dividing the pentagon into 5 isosceles triangles, calculating the area of one triangle, and then multiplying by 5. The side length used in area calculations is derived from the circle's radius and the angles of the triangle.
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Answered by CamilleEaton210 | 2024-10-11