Question

What is the area of a regular pentagon with a side length of 10 inches and a distance from the center to a vertex of 10 inches? Round your answer to the nearest tenth.

A. 242.5 in
B. 251.5 in
C. 228.5 in
D. 216.5

Answer 1

This equals 5 * the area of the triangle formed by the side and 2 lines from joining the center 2 the vertices.

Area of each triangle = 1/2 * base * height = 1/2 * 10 * (sqrt(10^2-5^2) = 43.30 ins^2

area of pentagon = 5* 43.30 = 216.5 in^2