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
819 ft.2
819 ft. squared
522 ft.2
522 ft. squared
148.5 ft.2
148.5 ft. squared
299.25 ft.2
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
1. Area of the base:
Since the base is a square, its area is side * side = 15 ft * 15 ft = 225 ft^2
2. Area of each triangular face:
The area of a triangle is 1/2 * base * height. In this case, the base of each triangular face is 15 ft and the height (perpendicular height) is given as 9.9 ft.
So, the area of each triangular face is 1/2 * 15 ft * 9.9 ft = 74.25 ft^2
3. Total surface area:
Now, we have one base with an area of 225 ft^2 and four triangular faces with an area of 74.25 ft^2 each. So, the total surface area is:
225 ft^2 (base) + 4 * 74.25 ft^2 (triangular faces) = 225 ft^2 + 297 ft^2 = 522 ft^2
Therefore, the correct answer is:
522 ft. squared