The pyramids right is 9.9 ft. And the bottom is 15 ft. Solve for the surface area of the square pyramid

Question

A. 522 ft.²
B. 299.25 ft.²
C. 819 ft.²
D. 148.5 ft.²

Answer 1

First, we need to find the slant height of the pyramid using the Pythagorean theorem:

s² = (15/2)² + 9.9²
s² = 7.5² + 9.9²
s² = 56.25 + 98.01
s² = 154.26
s ≈ 12.42 ft.

Now, we can calculate the surface area of the square pyramid using the formula:

Surface Area = Base Area + (0.5 * Perimeter * Slant Height)
Base Area = 15 ft * 15 ft = 225 ft²
Perimeter = 4 * 15 ft = 60 ft

Surface Area = 225 ft² + (0.5 * 60 ft * 12.42 ft)
Surface Area = 225 ft² + 372.6 ft²
Surface Area = 597.6 ft²

So, the correct answer is not listed, but the closest option is:

B. 299.25 ft.²