To calculate the surface area of a prism with a square base, we can use the formula:
\[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Area} \]
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Calculate the area of the base:
- The base is a square with a side length of 8 inches.
- Area of the base = \( \text{side}^2 = 8 \times 8 = 64 , \text{in}^2 \)
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Calculate the lateral area:
- The lateral area can be calculated using the perimeter of the base and the height of the prism.
- Perimeter of the base = \( 4 \times \text{side} = 4 \times 8 = 32 , \text{in} \)
- Lateral Area = Perimeter × Height = \( 32 \times 20 = 640 , \text{in}^2 \)
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Calculate the total surface area:
- Total Surface Area = \( 2 \times \text{Base Area} + \text{Lateral Area} \)
- Total Surface Area = \( 2 \times 64 + 640 = 128 + 640 = 768 , \text{in}^2 \)
The correct calculation for the surface area of the prism is 768 in².