What is the surface area of a square pyramid where the base edge is eight in the slant height is 16
To find the surface area of a square pyramid, we need to calculate the area of each of its four triangular faces and the area of its square base.
The base edge of the square pyramid is 8 inches, so the area of the base is (8 inches)^2 = 64 square inches.
The slant height is given as 16 inches. We can use the Pythagorean theorem to find the height of one of the triangular faces. Let's call it h.
Using the Pythagorean theorem:
h^2 + (8/2)^2 = 16^2
h^2 + 4^2 = 256
h^2 + 16 = 256
h^2 = 240
h ≈ √240 ≈ 15.49
The area of one triangular face is (1/2) * base * height, so the area of each of the four triangular faces is (1/2) * 8 * 15.49 = 61.96 square inches.
Therefore, the surface area of the square pyramid is 4 * 61.96 + 64 = 295.84 + 64 = 359.84 square inches.