To find the surface area of a rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
Given:
- Length \( l = 10 \) cm
- Width \( w = 3 \) cm
- Height \( h = 8 \) cm
Now, plug the values into the formula:
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Calculate \( lw \): \[ lw = 10 \times 3 = 30 , \text{cm}^2 \]
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Calculate \( lh \): \[ lh = 10 \times 8 = 80 , \text{cm}^2 \]
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Calculate \( wh \): \[ wh = 3 \times 8 = 24 , \text{cm}^2 \]
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Sum these areas: \[ lw + lh + wh = 30 + 80 + 24 = 134 , \text{cm}^2 \]
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Now multiply by 2 to get the total surface area: \[ \text{Surface Area} = 2 \times 134 = 268 , \text{cm}^2 \]
Therefore, the surface area of Gregory's rectangular prism is \( \boxed{268 , \text{cm}^2} \).