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
256 ft.2256 ft. squared
512 ft.2
To find the surface area of a square pyramid, we need to find the area of the base and the areas of the four triangular faces.
The area of the base can be found by calculating the square of the base edge, so the area of the base is 8 ft. × 8 ft. = 64 ft².
The area of each triangular face can be found by using the formula (1/2) × base × height, where the base is the base edge of the pyramid and the height is the slant height. So the area of each triangular face is (1/2) × 8 ft. × 16 ft. = 64 ft².
Since there are four triangular faces, the total area of the triangular faces is 4 × 64 ft² = 256 ft².
To calculate the surface area of the square pyramid, we add the area of the base and the areas of the triangular faces:
64 ft² (base) + 256 ft² (triangular faces) = 320 ft².
Therefore, the surface area of the square pyramid is 320 ft².