To find the surface area of the suitcase, which has the dimensions:
- Length \( l = 9.5 \) inches
- Width \( w = 16 \) inches
- Height \( h = 22.5 \) inches
The formula for the surface area \( A \) of a rectangular prism is:
\[ A = 2(lw + lh + wh) \]
Now, we will calculate each of the products:
- \( lw = 9.5 \times 16 = 152 \)
- \( lh = 9.5 \times 22.5 = 213.75 \)
- \( wh = 16 \times 22.5 = 360 \)
Now we sum these products:
\[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \]
Now we multiply by 2 to find the surface area:
\[ A = 2 \times 725.75 = 1451.5 \text{ in}^2 \]
Therefore, the surface area of the suitcase is:
1,451.5 in.²