To calculate the surface area \( S \) of a right rectangular prism, you can use the formula:
\[ S = 2(lw + lh + wh) \]
Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- \( l = 18 , \text{in} \),
- \( w = 12 , \text{in} \),
- \( h = 8 , \text{in} \).
Now, substituting the given values into the formula:
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Calculate \( lw \): \[ lw = 18 \times 12 = 216 , \text{in}^2 \]
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Calculate \( lh \): \[ lh = 18 \times 8 = 144 , \text{in}^2 \]
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Calculate \( wh \): \[ wh = 12 \times 8 = 96 , \text{in}^2 \]
Now, plug these values back into the surface area formula:
\[ S = 2(lw + lh + wh) = 2(216 + 144 + 96) \]
Now calculate the sum inside the parentheses:
\[ 216 + 144 + 96 = 456 \]
Finally, calculate the surface area:
\[ S = 2 \times 456 = 912 , \text{in}^2 \]
Thus, the surface area of the right rectangular prism is:
\[ \boxed{912 , \text{in}^2} \]
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