To find the surface area of a rectangular prism, we 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.
Given the dimensions of the rectangular prism are:
- Length (\( l \)) = 7 inches,
- Width (\( w \)) = 3 inches, and
- Height (\( h \)) = 11 inches.
We can plug these values into the formula:
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Calculate the area of each pair of opposite faces:
- \( lw = 7 \times 3 = 21 \)
- \( lh = 7 \times 11 = 77 \)
- \( wh = 3 \times 11 = 33 \)
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Now substitute these values back into the surface area formula: \[ \text{Surface Area} = 2(21 + 77 + 33) \]
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Calculate the sum inside the parentheses: \[ 21 + 77 + 33 = 131 \]
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Now multiply by 2: \[ \text{Surface Area} = 2 \times 131 = 262 \]
Thus, the surface area of the rectangular prism is 262 in².
The correct answer is:
262 in.²