Surface Area of Pyramids Quick Check

Question

3 of 53 of 5 Items
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

256 ft.2256 ft. squared

320 ft.2
320 ft. squared

512 ft.2512 ft. squared

Answer 1

To find the surface area of a square pyramid, you need to know the length of the base edge and the slant height.

The surface area can be calculated using the formula:

Surface Area = Base Area + (1/2 × Perimeter of the base × Slant Height)

In this case, the base of the pyramid is square, so the base area is equal to the side length squared:

Base Area = (8 ft)^2 = 64 ft^2

The perimeter of the base is equal to 4 times the length of one side:

Perimeter of the base = 4 × 8 ft = 32 ft

Now, substitute the values into the formula:

Surface Area = 64 ft^2 + (1/2 × 32 ft × 16 ft) = 64 ft^2 + (16 ft × 16 ft) = 64 ft^2 + 256 ft^2 = 320 ft^2

Therefore, the correct answer is:

320 ft.²