Question

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.

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.