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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

The base of the pyramid is a square, so the area of the base is found by squaring the length of one side. Since the base edge is 8 ft., the area of the base is 8^2 = 64 sq. ft.

Next, we need to find the area of each triangular face. Each face is a right triangle with one leg equal to the slant height and the other leg equal to half the base edge. The area of a triangle is given by the formula: A = (1/2)bh, where b is the base (half of the base edge) and h is the height (the slant height).

For each triangular face:
The base, b, is 8 ft. / 2 = 4 ft.
The height, h, is 16 ft.
The area, A, is (1/2)(4 ft.)(16 ft.) = 32 sq. ft.

Since there are 4 triangular faces, the total area of the triangular faces is 4 * 32 sq. ft. = 128 sq. ft.

Finally, we find the total surface area by summing the area of the base and the area of the triangular faces: 64 sq. ft. + 128 sq. ft. = 192 sq. ft.

Therefore, the surface area of the square pyramid is 192 sq. ft.

Answer 2

512 ft.2512 ft. squared  256 ft.2256 ft. squared  320 ft.2320 ft. squared128 ft.2

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize, but there seems to be an incorrect calculation in your response. The correct surface area of the square pyramid with a base edge of 8 ft. and a slant height of 16 ft. is:

To find the surface area, we first need to find the lateral area of the pyramid. The lateral area is the sum of the areas of the four triangular faces.

Each triangular face is an isosceles triangle with a base equal to the base edge, which is 8 ft., and two congruent side lengths equal to the slant height, which is 16 ft.

The area of each triangular face is (1/2) * base * height, where the base is 8 ft. and the height is 16 ft.

So, the area of each triangular face is (1/2) * 8 ft. * 16 ft. = 64 sq. ft.

Therefore, the total lateral area of the pyramid is 4 * 64 sq. ft. = 256 sq. ft.

Next, we need to find the area of the base. The base of the pyramid is a square with a side length of 8 ft.

The area of the base is 8 ft. * 8 ft. = 64 sq. ft.

Finally, to find the surface area, we add the lateral area to the area of the base: 256 sq. ft. + 64 sq. ft. = 320 sq. ft.

Therefore, the surface area of the square pyramid is 320 sq. ft.