To calculate the surface area of a rectangular suitcase, you can use the formula for the surface area \( SA \) of a rectangular prism:
\[ SA = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width, and
- \( h \) is the height.
Given:
- Length (\( l \)) = 9.5 inches
- Width (\( w \)) = 16 inches
- Height (\( h \)) = 22.5 inches
Now, plugging in the values:
\[ SA = 2( (9.5 \times 16) + (9.5 \times 22.5) + (16 \times 22.5) ) \]
Calculating each part:
- \( 9.5 \times 16 = 152 \)
- \( 9.5 \times 22.5 = 213.75 \)
- \( 16 \times 22.5 = 360 \)
Now, adding them together:
\[ 152 + 213.75 + 360 = 725.75 \]
Now multiply by 2:
\[ SA = 2 \times 725.75 = 1451.5 \text{ in}^2 \]
Thus, the surface area of the suitcase is:
\[ \boxed{1,451.5 \text{ in}^2} \]
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