To calculate the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
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Area of the base: Since the base is a square with edge length \( a = 8 \) ft, the area of the base \( A_{base} \) is: \[ A_{base} = a^2 = 8^2 = 64 \text{ ft}^2. \]
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Area of the triangular faces: Each triangular face has a base equal to the edge length of the square base and a height equal to the slant height \( l = 16 \) ft. The area of one triangular face \( A_{triangle} \) can be calculated as: \[ A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 16 = 64 \text{ ft}^2. \]
Since there are 4 triangular faces, the total area \( A_{triangles} \) for all four triangular faces is: \[ A_{triangles} = 4 \times A_{triangle} = 4 \times 64 = 256 \text{ ft}^2. \]
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Total surface area: The total surface area \( A_{total} \) of the pyramid is the sum of the base area and the total area of the triangular faces: \[ A_{total} = A_{base} + A_{triangles} = 64 + 256 = 320 \text{ ft}^2. \]
Thus, the surface area of the square pyramid is 320 ft².