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

148.5 ft.2
148.5 ft. squared

299.25 ft.2
299.25 ft. squared

522 ft.2
522 ft. squared

819 ft.2

1 answer

The surface area of a square pyramid can be found using the formula: base area + (1/2 x perimeter x slant height).

First, find the area of the square base:
Area = side^2 = 15^2 = 225 square feet

Next, calculate the slant height:
Slant height = sqrt(base side/2)^2 + height^2 = sqrt(15/2)^2 + 9.9^2 = sqrt(112.5 + 98.01) = sqrt(210.51) = 14.51 feet

Finally, find the surface area:
Surface area = base area + (1/2 x perimeter x slant height)
Surface area = 225 + (1/2 x 4 x 15 x 14.51) = 225 + 436.5 = 661.5 square feet

Therefore, the surface area of the square pyramid is 661.5 ft^2.