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.
In your case, you provided the dimensions as \( l = 7 \) in, \( w = 5 \) in, and \( h = 15 \) in.
Let’s substitute these values into the formula:
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Calculate \( lw \): \[ lw = 7 , \text{in} \times 5 , \text{in} = 35 , \text{in}^2 \]
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Calculate \( lh \): \[ lh = 7 , \text{in} \times 15 , \text{in} = 105 , \text{in}^2 \]
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Calculate \( wh \): \[ wh = 5 , \text{in} \times 15 , \text{in} = 75 , \text{in}^2 \]
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Now, substitute these into the surface area formula: \[ \text{Surface Area} = 2(35 + 105 + 75) \]
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Calculate the sum inside the parentheses: \[ 35 + 105 + 75 = 215 , \text{in}^2 \]
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Finally, multiply by 2: \[ \text{Surface Area} = 2 \times 215 = 430 , \text{in}^2 \]
Therefore, the surface area of the prism is \( \boxed{430} \) in².