To calculate the surface area of a prism with a square base, we can use the following formula:
\[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Area} \]
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Calculate the base area: For a square base, the area is given by: \[ \text{Base Area} = \text{side length}^2 = 8^2 = 64 \text{ in}^2 \]
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Calculate the lateral area: The lateral area of a prism is given by the perimeter of the base multiplied by the height:
- Perimeter of the square base: \[ \text{Perimeter} = 4 \times \text{side length} = 4 \times 8 = 32 \text{ in} \]
- Lateral Area: \[ \text{Lateral Area} = \text{Perimeter} \times \text{height} = 32 \times 20 = 640 \text{ in}^2 \]
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Combine the areas: Now, use the areas to find the total surface area: \[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Area} = 2 \times 64 + 640 = 128 + 640 = 768 \text{ in}^2 \]
Thus, the correct answer for the surface area of the prism is:
768 in. squared.