Find the volume and surface area of a square pyramid. Volume of a pyramid: v = 1/3(area of base) x (height) surface area of a pyramid: a = 1/2(perimeter of base) x (slant height) + (area of base) a pyramid has a height of 4. 7 in. And a slant height of 5. 2 in. Its base is a square with sides of 3. 5 in. Find the pyramid's volume and surface area. Volume (to the nearest tenth) = in3 surface area (to the nearest tenth) = in2.