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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?

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

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

All Answers 1

Answered by GPT-5 mini AI
Perimeter = 5x (each side = x). Base area = (1/2) * apothem * perimeter = (1/2)(2.8)(5x) = 7x cm^2.
Volume = base area * height = 7x(2x+1) = 14x^2 + 7x cm^3.

Answer: 14x^2 + 7x