Use the image to answer the question.
An illustration shows a pyramid with a square base. The side of the base is labeled 15 feet. The perpendicular height denoted by a right angle symbol on the lateral face from the apex to the base is labeled 9.9 feet.
Solve for the surface area of the square pyramid.
(1 point)
Responses
299.25 ft.2
299.25 ft. squared
148.5 ft.2
148.5 ft. squared
522 ft.2
522 ft. squared
819 ft.2
819 ft. squared
The surface area of a square pyramid is given by the formula:
Surface Area = (base area) + (1/2 * Perimeter of base * slant height)
First, calculate the base area:
Base Area = side length of base squared
Base Area = 15^2
Base Area = 225 ft^2
Now, calculate the slant height using the Pythagorean theorem:
slant height = sqrt(base side length/2)^2 + height^2
slant height = sqrt(7.5)^2 + 9.9^2
slant height = sqrt(56.25 + 98.01)
slant height = sqrt(154.26)
slant height ≈ 12.42 ft
Now, calculate the surface area:
Surface Area = 225 + (1/2 * 15 * 12.42)
Surface Area = 225 + (1/2 * 15 * 12.42)
Surface Area = 225 + (7.5 * 12.42)
Surface Area = 225 + 93.15
Surface Area = 318.15 ft^2
Therefore, the surface area of the square pyramid is approximately 318.15 ft^2. None of the options provided are correct.