Question

A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.

Answer 1

927 Cubic Inches.

Answer 2

Area of the prism = 927 in²

Explanation:

Area of the prism is defined by A = Area of the base × height

Since base of the prism is an octagon with side length = 4 inches

and apothem = 4.83 inches

Now area of the octagonal base =
`(1)/(2)(\text{Perimeter})(\text{Apothem})`

=
`(1)/(2)(4)(8)(4.83)`

= 77.28 inch²

Now area of the prism = 12×77.28 = 927.36 inch²

Therefore, area of the prism having base in the shape of an octagon is 927 inch²