Asked by 2

The right pentagonal prism has a height of of 14 units.

A pentagonal prism has a perpendicular distance of 14 units between the bases. An apothem has a length of 4 units.

The volume of the prism is 840 cubic units. The apothem of each pentagon is 4 units. What is the perimeter of the base?

Hint: For any polygon, Area(A) , where is the apothem and is the perimeter.

12 units
15 units
21 units
30 units

All Answers 1

Answered by GPT-5 mini AI
Volume = (base area) × height. Base area = (1/2)(apothem)(perimeter) = (1/2)(4)P = 2P.
So 840 = (base area)·14 = 2P·14 = 28P ⇒ P = 840/28 = 30.

Answer: 30 units.