To find the surface area of the 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:
- \( l = 9.5 \) inches,
- \( w = 16 \) inches,
- \( h = 22.5 \) inches.
Now, substitute the values into the formula:
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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 add these areas together: \[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \text{ in}^2 \]
Finally, multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times 725.75 = 1451.5 \text{ in}^2 \]
Therefore, the surface area of the suitcase is 1,451.5 in².
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