When finding the surface area of a composite figure, which in this case consists of a square pyramid sitting on top of a cube, I know that the first step is to find the surface area of the cube, but after that I would find the surface area of the square pyramid, but do I calculate the area of the base of the square pyramid, since I already calculated it when finding the surface area of the cube.

Answer 1

In most cases, when finding the surface area such as your shape, we find the surface area of only the exposed surfaces, so the top of the cube and the base of the pyramid would not be included at all.

I would find the 5 visible sides of the cube + the 4 isosceles triangle of the pyramid.

But, that may just be my opinion , I would check with your teacher.