Suppose we have a pyramid with a triangular base and there is another pyramid with a triangular base that is inside the first one I mentioned. So you can imagine a smaller sphere being in a big sphere and how it works. Now try picturing it with pyramids with triangular bases.
Prove that the surface area of the outside pyramid is greater then the surface area of the inside pyramid and prove that the perimeter of the outside pyramid is greater then the perimeter of the inside pyramid.
This problem seems so obvious visually that I am unsure how to show it. A couple of ideas I had was to unfold each pyramid or flatten it onto a plane then try to get some pattern I can find from the pyramid to the one inside it. Another idea was to consider the formulas for the surface area of a pyramid with a triangular base and see if that would show anything.