Use the image to answer the question.

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

522 ft.2
522 ft. squared

299.25 ft.2
299.25 ft. squared

819 ft.2
819 ft. squared

148.5 ft.2

Answer 1

To find the surface area of a square pyramid, we first find the lateral area and add it to the base area.

Lateral area = 0.5 * perimeter of base * slant height
Base area = side of base^2

Perimeter of base = 4 * side of base = 4 * 15 = 60 ft
Slant height = sqrt(9.9^2 + (15/2)^2) = sqrt(98.01 + 56.25) = sqrt(154.26) = 12.42 ft

Lateral area = 0.5 * 60 * 12.42 = 372.6 ft^2
Base area = 15^2 = 225 ft^2

Surface area = 372.6 + 225 = 597.6 ft^2

Therefore, the surface area of the square pyramid is approximately 597.6 ft^2. None of the given options match this result, so the correct answer is not provided.