To calculate the surface area of a prism with a square base, you can use the formula:
\[ \text{Surface Area} = 2B + Ph \]
where:
- \(B\) is the area of the base,
- \(P\) is the perimeter of the base, and
- \(h\) is the height of the prism.
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Calculate the base area (B):
- The base is square, so the area \(B\) is given by: \[ B = \text{side}^2 = 8 , \text{in} \times 8 , \text{in} = 64 , \text{in}^2 \]
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Calculate the perimeter (P):
- The perimeter of a square is given by: \[ P = 4 \times \text{side} = 4 \times 8 , \text{in} = 32 , \text{in} \]
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Use the height (h):
- Given height \(h = 20 , \text{in}\).
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Plug these values into the surface area formula: \[ \text{Surface Area} = 2B + Ph = 2(64 , \text{in}^2) + (32 , \text{in} \times 20 , \text{in}) \]
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Calculate \(2B\): \[ 2B = 2 \times 64 , \text{in}^2 = 128 , \text{in}^2 \]
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Calculate \(Ph\): \[ Ph = 32 , \text{in} \times 20 , \text{in} = 640 , \text{in}^2 \]
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Add the two results to find the total surface area: \[ \text{Surface Area} = 128 , \text{in}^2 + 640 , \text{in}^2 = 768 , \text{in}^2 \]
Therefore, the surface area of the prism is \(768 , \text{in}^2\).