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 320 ft.2 320 ft. squared 512 ft.2512 ft. squared 256 ft.2

Answer 1

The surface area of a square pyramid can be found using the formula:

Surface Area = base area + lateral area

The base area of the square pyramid is given by the formula:

Base Area = (edge length)^2

In this case, the edge length is 8 ft., so the base area is:

Base Area = (8 ft.)^2 = 64 ft.²

The lateral area of the square pyramid is given by the formula:

Lateral Area = (1/2) * perimeter * slant height

The perimeter of the base of a square pyramid is equal to 4 times the edge length, so in this case, the perimeter is:

Perimeter = 4 * 8 ft. = 32 ft.

Using the given slant height of 16 ft., the lateral area is:

Lateral Area = (1/2) * 32 ft. * 16 ft. = 256 ft.²

Therefore, the total surface area of the square pyramid is:

Surface Area = 64 ft.² + 256 ft.² = 320 ft.²