Question

Question

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

512 ft.2512 ft. squared

320 ft.2
320 ft. squared

128 ft.2
128 ft. squared

256 ft.2

Answer 1

To find the surface area of a square pyramid, we need to calculate the sum of the areas of the base and the four triangular faces.

The area of the base can be found by multiplying the length of one side of the base by itself. In this case, the base edge is 8 ft, so the area of the base is 8 * 8 = 64 ft^2.

To find the area of the triangular faces, we can use the formula A = (1/2)bh, where b is the base of the triangle and h is the height. In this case, the base of each triangular face is 8 ft and the height can be found using the Pythagorean theorem. The height is the altitude of the triangle, which can be found by using the length of the slant height and the side length of the base.

Using the Pythagorean theorem, we can find the height of the triangular face: h = sqrt((slant height)^2 - (base/2)^2) = sqrt(16^2 - 4^2) = sqrt(256 - 16) = sqrt(240) ≈ 15.49 ft.

Now we can calculate the area of one triangular face: A = (1/2)(8 ft)(15.49 ft) ≈ 61.96 ft^2.

Since there are four triangular faces, the total area of the triangular faces is 4 * 61.96 ft^2 = 247.84 ft^2.

Adding the area of the base and the area of the triangular faces, we get the total surface area: 64 ft^2 + 247.84 ft^2 = 311.84 ft^2.

Therefore, the surface area of the square pyramid is approximately 311.84 ft^2.

None of the given answer choices match this result, so there may be a mistake in the provided options.