Question

A rectangular pyramid and a rectangular prism have bases of the same dimensions as shown below.



The surface area of the rectangular pyramid is 174 square inches. The height of the rectangular prism is the same as the slant height of the pyramid. What is the surface area of the rectangular prism?

234 in2

148 in2

254 in2

348 in2

Answer 1

This is a bit complicated. But the two solids have the same base, which simplifies things quite a bit. The rectangular prism and pyramid have length and width where both are them same.

Let the slant height = s
The surface area of the pyramid is given as 174
174 = 2 * 1/2 s (l) + 2 * 1/2 s (w) = s(l + w)

that's assuming that we're not counting the area of the base, but in the end I think it won't matter, because the two solids have the same base.

The height of the prism is equal to s
so the area of the 4 sides of the prism is s(2l + 2w)

I'm still not sure how to deal with the top of the box.

Answer 2

So far, we have a lateral area for the prism that is twice that of the pyramid. The question remaining is whether we count the area of the top of the box. But I think lateral area is only lateral, that is, sideways. Are you OK with this?

Answer 3

So I think we have an answer, if you are following what I've said.