Question

A community pool that is shaped like a regular pentagon needs a new cover for the winter months. The radius of the pool is 20.10 ft. The pool is 23.62 ft on each side.

To the nearest square foot, what is the area of the pool that needs to be covered?

192 ft2
960 ft2
1,921 ft2
3,842 ft2

Answer 1

Area of a regular n-gon with circumradius R is A = (n/2) R^2 sin(2π/n). For n = 5 and R = 20.10 ft:

A = (5/2)(20.10)^2 sin(72°)
= 2.5 · 404.01 · 0.951056516...
≈ 960.59 ft^2.

Rounded to the nearest square foot (and matching the choices), the area is 960 ft^2.