Find the volume of a prism with triangular bases where the perimeter of the base = 16", apothem = x", and the prism height = 10". Use V = Bh and A = 1/2 ap for the area of the base.

Question

Mathematics

Reid Peters

24 November, 01:07

Find the volume of a prism with triangular bases where the perimeter of the base = 16", apothem = x", and the prism height = 10". Use V = Bh and A = 1/2 ap for the area of the base.

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Answers (1)

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Elijah Freeman · Answer 1

First, calculate for the area of the base by the equation given,

A = 1/2aP

where A is area, a is apothem, and P is perimeter. Substituting the known values,

A = 1/2 (x) (16") = 8x in²

Next, solve for the volume of the prism by the equation,

V = Bh = (8x in²) (10 in)

V = 80x in³

Thus, the volume of the prism is approximately 80x in³.