The volume of a triangular pyramid is 13.5 cubic meters. What is the volume of a triangular prism with a congruent base and the same height?

The prism is 3 by 3 by 1.5.

Step-by-step explanation:

The prism has a length x and a width x. Since it is a square at the base both length and width are the same amount x. The height is "half the length of one edge of the base". Since the base is x, this makes it 1/2x.

The volume's prism is found using V = l*w*h. Substitute and simplify.

13.5 = x*x*1/2x

13.5 = 1/2 x^3

27 = x^3

3 = x

The prism is 3 by 3 by 1.5.

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