What is the surface area of the square permit where the base edge is? 8 feet in the slant height is 16 feet
The slant height is the hypotenuse of a right triangle with the base edge as one of the legs. Using the Pythagorean theorem, we can find the other leg of the triangle.
The other leg is the height of the square pyramid. Let's call it "h".
Using the Pythagorean theorem:
h^2 + (8 ft)^2 = (16 ft)^2
h^2 + 64 ft^2 = 256 ft^2
h^2 = 192 ft^2
h = √192 ft
h ≈ 13.86 ft
Now, let's find the surface area of the square pyramid using the formula:
Surface Area = base area + 4 * (0.5 * base edge * slant height)
The base area is the area of a square with side length 8 ft:
Base Area = (8 ft)^2 = 64 ft^2
Surface Area = 64 ft^2 + 4 * (0.5 * 8 ft * 16 ft)
Surface Area = 64 ft^2 + 4 * 64 ft^2
Surface Area = 64 ft^2 + 256 ft^2
Surface Area = 320 ft^2
Therefore, the surface area of the square pyramid is 320 square feet.