Side height 9.9 ft. width Base 15 ft.
Solve for the surface area of the square pyramid
To find the surface area of the square pyramid, we need to calculate the area of each of the faces and then add them together.
First, we need to find the area of the base of the pyramid, which is a square with a side length of 15 ft. The formula to find the area of a square is side length squared, so the area of the base is 15 ft * 15 ft = 225 square feet.
Next, we need to find the area of the four triangular faces of the pyramid. Since the pyramid is a square pyramid, all four triangular faces are congruent and have the same area. Each triangular face is a right triangle with a base of 15 ft (which is half of the side length of the square base) and a height of 9.9 ft. The formula to find the area of a triangle is 1/2 * base * height, so the area of each triangular face is (1/2) * 15 ft * 9.9 ft = 74.25 square feet.
Since there are four triangular faces, the total area of all the triangular faces is 4 * 74.25 = 297 square feet.
Finally, to find the total surface area of the square pyramid, we add the area of the base and the area of the four triangular faces:
225 square feet (base) + 297 square feet (triangular faces) = 522 square feet
Therefore, the surface area of the square pyramid is 522 square feet.