To calculate the surface area of a square pyramid, we need to consider both the area of the base and the area of the four triangular faces.
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Area of the base:
- The base is a square with a side length of 15 feet.
- Area of the base = side × side = \( 15 , \text{ft} \times 15 , \text{ft} = 225 , \text{ft}^2 \)
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Area of the triangular faces:
- Each triangular face has a base of 15 feet and a height of 9.9 feet (the height from the apex to the midpoint of the base of the triangle, which is also the height of the triangle).
- Area of one triangular face = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 15 , \text{ft} \times 9.9 , \text{ft} = 74.25 , \text{ft}^2 \)
- Since there are 4 triangular faces, the total area of the triangular faces = \( 4 \times 74.25 , \text{ft}^2 = 297 , \text{ft}^2 \)
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Total surface area of the pyramid:
- Total surface area = Area of base + Area of triangular faces
- Total surface area = \( 225 , \text{ft}^2 + 297 , \text{ft}^2 = 522 , \text{ft}^2 \)
Therefore, the surface area of the square pyramid is 522 ft².
The correct response is: 522 ft.²