Question

A square prism and square pyramid have the same base and the same surface area. Show that the slant height, l, of the pyramid is l=5/2 x s where s is the length of the base.

Answer 1

If the height of the prism is h, then its area is 2s^2+4sh

If the pyramid has slant height l, then its area is s^2 + 4sl

So, we just need to solve for l in

2s^2+4sh = s^2+4sl
s^2+4sh = 4sl

Hmm. It appears that by "square prism" you mean "cube," since in that case

5s^2 = 4sl
5s = 4l
l = 5/4 s

Check for typos - mine, or in the problem...

Answer 2

There are no typos but a square prism is a rectangular prism

Answer 3

I mean its like a rectangular prism but with squares as the base