What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?(1 point) Responses 128 ft.2 128 ft. squared 512 ft.2512 ft. squared 256 ft.2256 ft. squared 320 ft.2
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base would be the square of the side length, which is 8 ft. So the area of the base is 8^2 = 64 ft^2.
To find the area of each triangular face, we can use the formula for the area of a triangle: (base * height) / 2.
In this case, the base of each triangular face is the edge length of the square base, which is 8 ft, and the height is the slant height, which is 16 ft.
So the area of each triangular face is (8 * 16) / 2 = 64 ft^2.
Since there are four triangular faces, the total area of the four triangular faces is 4 * 64 = 256 ft^2.
Adding the area of the base and the area of the four triangular faces together, we get the total surface area of the pyramid: 64 + 256 = 320 ft^2.
Therefore, the answer is 320 ft^2.