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)

Question

Responses

128 ft.2
128 ft. squared

320 ft.2
320 ft. squared

256 ft.2256 ft. squared

512 ft.2512 ft. squared

Answer 1

To find the surface area of a square pyramid, we need to find the area of the base and the area of each triangular face.

The base of the pyramid is a square, so the area of the base is found by squaring the length of one side. In this case, the base edge is 8 ft., so the area of the base is 8^2 = 64 ft^2.

Each face of the pyramid is a triangle. To find the area of a triangle, we can use the formula: area = (1/2) * base * height. In this case, the base of each triangular face is the base edge of the pyramid, which is 8 ft. The height of each triangular face is the slant height of the pyramid, which is 16 ft.

So, the area of each triangular face is (1/2) * 8 * 16 = 64 ft^2.

Since there are 4 triangular faces, the total area of the triangular faces is 4 * 64 = 256 ft^2.

To find the total surface area of the pyramid, we add the area of the base to the area of the triangular faces: 64 + 256 = 320 ft^2.

Therefore, the correct answer is:

320 ft.2