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
148.5 ft.2
148.5 ft. squared
522 ft.2
522 ft. squared
299.25 ft.2
299.25 ft. squared
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To find the surface area of a square pyramid, we need to calculate the area of the base and the area of each triangular face.
1. Area of the base:
Since the base is a square, we can find the area by squaring the side length:
Area of the base = 15 ft * 15 ft = 225 ft²
2. Area of each triangular face:
To find the area of a triangular face, we use the formula: (1/2) * base * height
In this case, the base of each triangular face is the side length of the square base (15 ft) and the height is the perpendicular height (9.9 ft):
Area of each triangular face = (1/2) * 15 ft * 9.9 ft = 74.25 ft²
Since there are 4 triangular faces in a square pyramid, we multiply this area by 4:
Total area of the triangular faces = 4 * 74.25 ft² = 297 ft²
3. Total surface area:
Total surface area = Area of the base + Total area of the triangular faces
Total surface area = 225 ft² + 297 ft² = 522 ft²
Therefore, the surface area of the square pyramid is 522 ft².
choes one of the options
522 ft.2
522 ft. squared