To find the surface area of a rectangular suitcase, we can use the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length \( l = 9.5 \) inches,
- Width \( w = 16 \) inches,
- Height \( h = 22.5 \) inches.
We will calculate:
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Calculate \( lw \): \[ lw = 9.5 \times 16 = 152 \text{ in}^2 \]
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Calculate \( lh \): \[ lh = 9.5 \times 22.5 = 213.75 \text{ in}^2 \]
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Calculate \( wh \): \[ wh = 16 \times 22.5 = 360 \text{ in}^2 \]
Now, plug these values into the surface area formula: \[ \text{Surface Area} = 2(152 + 213.75 + 360) \]
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Calculate the sum \( (lw + lh + wh) \): \[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \text{ in}^2 \]
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Now multiply by 2: \[ \text{Surface Area} = 2 \times 725.75 = 1451.5 \text{ in}^2 \]
Thus, the surface area of the suitcase is: \[ \boxed{1,451.5 , \text{in}^2} \]