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 = (s^(2)n)/(4 tan\left ( (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 = (3^(2)(5))/(4 tan\left ( (180)/(5) \right ))\\\\\\area of pentagon = (9(5))/(4 tan\left ( 36 \right ))\\\\area of pentagon = (45)/(4 ( 0.7265 ))\\\\area of pentagon = (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