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
522 ft.2
819 ft.2
299.25 ft.2
To find the surface area of a square pyramid, we need to find the area of the base and add the areas of the four triangular faces.
The area of the base square is side^2 = 15^2 = 225 ft^2.
Each triangular face has a base equal to the side of the square base (15 ft) and a height equal to the perpendicular height from the apex to the base (9.9 ft).
The area of each triangular face is 0.5 * base * height = 0.5 * 15 * 9.9 = 74.25 ft^2.
Since there are four triangular faces, the total area of the triangular faces is 4 * 74.25 = 297 ft^2.
So, the total surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
225 + 297 = 522 ft^2.
Therefore, the correct answer is 522 ft^2.