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

320 ft.2
320 ft. squared

128 ft.2
128 ft. squared

512 ft.2512 ft. squared

256 ft.2

Answer 1

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 is calculated by finding the square of the base edge length, which is 8 ft. So, the area of the base is 8 ft. x 8 ft. = 64 ft².

To find the area of the four triangular faces, we need to use the slant height, which is 16 ft. and the base edge length, which is 8 ft.

Using the formula for the area of a triangle, which is 1/2 x base x height, we can find the area of one triangular face.

The height of the triangle can be found using the Pythagorean theorem:
height^2 = (slant height)^2 - (base/2)^2
height^2 = 16 ft.² - (8 ft./2)^2
height^2 = 16 ft.² - 16 ft.²
height^2 = 0 ft.²
height = 0 ft.

Since the height is 0, the triangular face is actually a line segment, so it does not have an area.

Therefore, the surface area of the square pyramid is the area of the base, which is 64 ft².

So the correct answer is 64 ft².

Answer 2

pick one of the answer choices i gave you

Answer 3

The correct answer is 320 ft².