The four slant edges of the truncated pyramid will be touching the cone within which it is inscribed. Thus, the diameter of the cone at some height is equal to the diagonal of the square pyramid. If you know the diagonal of a square, then what are the side lengths?

Once you have the side lengths of the top and bottom of the truncated pyramid, you know the area of the top and bottom, the square portions. What shape are the sides of the truncated pyramid? How can you find their areas?