Question

A pentagonal prism has a height of 9 feet, and each base edge is 3 feet. Find the volume. Round your answer to the nearest hundredth.

Answer 1

The volume is 139.36ft^3

Answer 2

Height of the pentagon = 9 ft

Edge of base = 3 ft

$area of pentagon = \frac{s^{2}n}{4 tan\left ( \frac{180}{n} \right )}$

s is the length of any side = 3

n is the number of sides = 5

tan is the tangent function calculated in degrees

$\\ \\\\area of pentagon = \frac{3^{2}(5)}{4 tan\left ( \frac{180}{5} \right )}\\\\\\area of pentagon = \frac{9(5)}{4 tan\left ( 36 \right )}\\\\area of pentagon = \frac{45}{4 ( 0.7265 )}\\\\area of pentagon = \frac{45}{2.906}\\\\area of pentagon = 15.4852$

Volume of the pentagon = area of base (height )

Volume of the pentagon = 15.4852 (9)

Volume of the pentagon = 139.366

Volume of the pentagon = 139.37 cu.ft