Question

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

512 ft.^2

128 ft.^2

320 ft.^2

256 ft.^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate 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 can be found by taking the square of the length of the base edge. In this case, the base edge is 8 ft, so the area of the base is 8^2 = 64 ft^2.

The area of each triangular face can be found by using the formula: (1/2) * base * height. In this case, the base of each triangular face is the same as the length of the base edge, which is 8 ft. The height of each triangular face is the slant height, which is 16 ft. So the area of each triangular face is (1/2) * 8 ft * 16 ft = 64 ft^2.

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

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

So, the correct answer is 320 ft^2.