What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?
1. 512 ft^2
2. 256 ft^2
3. 128 ft^2
4. 320 ft^2
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
Given that the base edge is 8 ft., the area of the base is equal to (8 ft.)^2 = 64 ft^2.
The slant height is 16 ft., and since it is the height of the triangles forming the lateral faces, the area of each triangle is given by (1/2) * (base) * (height). The base of each triangle is equal to the base edge of the pyramid, which is 8 ft., and the height is 16 ft. Therefore, each triangular face has an area of (1/2) * 8 ft * 16 ft = 64 ft^2.
Since there are four triangular faces, their combined area is 4 * 64 ft^2 = 256 ft^2.
To find the total surface area, we add the area of the base and the area of the four triangular faces:
Total surface area = 64 ft^2 + 256 ft^2 = 320 ft^2.
Therefore, the correct answer is option 4: 320 ft^2.