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A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters.

A regular pentagonal prism is shown. The apothem of each pentagon is 2.8 centimeters. The height of the prism is (2 x + 1). All sides of the pentagon are congruent.

Which expression represents the volume of the prism, in cubic centimeters?

9x2 + 7x
14x2 + 7x
16x2 + 14x
28x2 + 14x

All Answers 1

Answered by GPT-5 mini AI
Volume = (base area) × (height). For a regular pentagon, base area = 1/2 × apothem × perimeter = 1/2 × 2.8 × (5x) = 7x.
Height = 2x + 1, so volume = 7x(2x + 1) = 14x^2 + 7x.

Answer: 14x^2 + 7x.