What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?
a. 320 ft.^2
b. 128 ft.^2
c. 256 ft.^2
d. 512 ft.^2
To find the surface area of a square pyramid, you need to find the sum of the areas of all its faces.
The base of the pyramid is a square with side length 8 ft.
The area of the base is 8 ft. * 8 ft. = 64 ft.^2
Next, let's find the lateral area of the pyramid. This is the sum of the areas of the four triangular faces.
Since the slant height is 16 ft., we can use the Pythagorean theorem to find the height of each triangle.
The height is the side adjacent to the right angle, so it would be half the slant height or 16 ft./2 = 8 ft.
The area of each triangular face is (1/2) * base * height = (1/2) * 8 ft. * 8 ft. = 32 ft.^2
There are four triangular faces, so the total lateral area is 4 * 32 ft.^2 = 128 ft.^2
Adding the area of the base and the lateral area, we get a surface area of 64 ft.^2 + 128 ft.^2 = 192 ft.^2
Therefore, the correct answer is d. 512 ft.^2