Question

A side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches. What is the area of a cross-section of the prism? What is the volume of the prism?

A) 12 in2; 216 in3 B) 24 in2; 432 in3 C) 60 in2; 1080 in3
D) 120 in2; 2160 in3

Answer 1

Your answer will be C) 60 in²; 1080 in³

Answer 2

Area and volume of pentagonal prism is 660 inches² and 1080 inches³

Explanation:

Given : A pentagonal prism having side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches.

We have to calculate

1) area of a cross-section of the prism

2) the volume of the prism

1) Area of cross section of pentagonal prism =5ab +5bh

Where a = apothem

b - base length

h = height.

For the given pentagon

apothem = 4 inches

base = 6 inches

Height = 18 inches

Area of cross section of pentagonal prism =5 ×4 × 6 + 5× 6 × 18

Area of cross section of pentagonal prism = 120 + 540

Area of cross section of pentagonal prism = 660 inches²

2) Volume of pentagonal prism =
`(AP)/(2) * H`

Where, A = apothem

P is perimeter of base

H= height

Perimeter of pentagon is 5b = 30 inches

Volume of pentagonal prism =
`(4* 30)/(2) * 18`

Volume of pentagonal prism = 1080 inches³

Thus, Area and volume of pentagonal prism is 660 inches² and 1080 inches³.