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Correct  V = 82.5 in³

Step-by-step explanation:

This is a regular five sided prism.

Given:

The base edge  a = 4 in

The radius of the inscribed circle or the height of an isosceles triangle

Ri = h = 2.75 in

Prism height   H = 3 in

The base consists of five isosceles triangles

The area of one triangle is:

A₁ = a · h / 2

The area of the base is:

B = 5 · A₁ = 5 · a · h / 2

B = 5 · 4 · 2.75 / 2 = 27.5 in²

The volume of the prism is:

V = B · H = 27.5 · 3 = 82.5 in³

V = 82.5 in³

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