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
320 ft.2
320 ft. squared
512 ft.2512 ft. squared
256 ft.2256 ft. squared
128 ft.2
To find the surface area of a square pyramid, you need to find the area of each face and then sum them up.
The base of the pyramid is a square, so the area of the base is calculated by taking the square 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.
Now let's find the area of the slanted faces. The slant height is given as 16 ft., which is the height of each triangle face. The base of each triangle face is the same as the base edge of the pyramid, which is 8 ft. The formula to find the area of a triangle is (base * height) / 2.
So, for each triangle face, the area is (8 * 16) / 2 = 64 ft^2.
Since there are 4 triangle faces in a square pyramid, the total area of the triangle faces is 4 * 64 = 256 ft^2.
The surface area of the square pyramid is the sum of the base area and the area of the triangle faces. Therefore, the surface area is 64 ft^2 + 256 ft^2 = 320 ft^2.
Therefore, the correct answer is 320 ft^2.