what is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?
a 512 ft.^2
b 320 ft.^2
c 256 ft.^2
d 128 ft.^2
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangles that make up the walls of the pyramid.
The area of the base of a square pyramid is given by the formula:
Base Area = (side length)^2
In this case, the base edge is 8 ft, so the base area is 8^2 = 64 ft^2.
The area of each triangle is given by the formula:
Triangle Area = (base length * height) / 2
In this case, the base length is 8 ft and the slant height is 16 ft. To find the height of the triangle, we can use the Pythagorean theorem:
(height)^2 + (base length/2)^2 = (slant height)^2
(height)^2 + (8/2)^2 = 16^2
(height)^2 + 4^2 = 16^2
(height)^2 + 16 = 256
(height)^2 = 256 - 16
(height)^2 = 240
(height) ≈ √240 ≈ 15.49 ft
Now we can find the area of each triangle:
Triangle Area = (8 ft * 15.49 ft) / 2 ≈ 61.96 ft^2
Since there are four triangles, the total area of the triangles is:
4 * 61.96 ft^2 = 247.84 ft^2
Finally, we can find the surface area of the square pyramid by adding the base area and the area of the triangles:
Surface Area = Base Area + Total Triangle Area = 64 ft^2 + 247.84 ft^2 = 311.84 ft^2
Rounded to the nearest whole number, the surface area of the square pyramid is 312 ft^2.
None of the given answer choices are correct, so there may be a mistake in the problem or the options listed.