To calculate the surface area of a square pyramid, we can use the formula:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} \]
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Base Area: For a square pyramid, the base area is given by: \[ \text{Base Area} = \text{side}^2 \] Given the base edge is 8 ft: \[ \text{Base Area} = 8^2 = 64 \text{ ft}^2 \]
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Lateral Area: The lateral area of a pyramid is the sum of the areas of its four triangular faces. The area of one triangular face can be calculated with: \[ \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base of each triangular face is the side of the square base (which is 8 ft) and the height is the slant height (which is 16 ft): \[ \text{Area of one triangular face} = \frac{1}{2} \times 8 \times 16 = \frac{128}{2} = 64 \text{ ft}^2 \] Since there are 4 triangular faces: \[ \text{Lateral Area} = 4 \times 64 = 256 \text{ ft}^2 \]
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Total Surface Area: Now we can add the base area and the lateral area together: \[ \text{Surface Area} = 64 \text{ ft}^2 + 256 \text{ ft}^2 = 320 \text{ ft}^2 \]
Therefore, the surface area of the square pyramid is 320 ft².
The correct response is: 320 ft.2 or 320 ft. squared.