To calculate the surface area of a prism with a square base, we can use the formula:
\[ \text{Surface Area} = 2 \cdot \text{Base Area} + \text{Lateral Surface Area} \]
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Calculate the area of the base: Since the base is a square with a side length of \( s = 8 \) inches: \[ \text{Base Area} = s^2 = 8^2 = 64 \text{ in}^2 \]
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Calculate the lateral surface area: The lateral surface area of a prism with a square base consists of the areas of the four rectangular sides. Each of these rectangles has a width equal to the side length of the base and a height equal to the height of the prism (\( h = 20 \) inches): \[ \text{Lateral Surface Area} = 4 \cdot (s \cdot h) = 4 \cdot (8 \cdot 20) = 4 \cdot 160 = 640 \text{ in}^2 \]
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Putting it all together: The total surface area is: \[ \text{Surface Area} = 2 \cdot \text{Base Area} + \text{Lateral Surface Area} \] \[ = 2 \cdot 64 + 640 = 128 + 640 = 768 \text{ in}^2 \]
The correct calculation for the surface area of the prism is 768 in².