base edge: 15 ft

Question

height: 9.9 ft

Solve for the surface area of the square pyramid

a. 299.25 ft. ^3
b. 522 ft. ^2
c. 819 ft.^2
d. 148.5 ft.^2

Answer 1

The surface area of a square pyramid can be found using the formula:

Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)

First, calculate the base area:
Base Area = 15 ft * 15 ft = 225 ft^2

Now, calculate the perimeter of the base:
Perimeter of Base = 4 * 15 ft = 60 ft

Next, calculate the slant height using the Pythagorean theorem:
Slant Height = √(15 ft)^2 + (9.9 ft)^2 ≈ 18.19 ft

Now plug the values into the formula:
Surface Area = 225 ft^2 + (0.5 * 60 ft * 18.19 ft) = 225 ft^2 + 545.7 ft^2 = 770.7 ft^2

Therefore, the correct answer is not listed, but it's closest to 770.7 ft^2.