To calculate the surface area of the suitcase, which is a rectangular prism, 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, and \(h\) is the height.
Given:
- \(l = 9.5\) inches
- \(w = 16\) inches
- \(h = 22.5\) inches
First, we 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:
\[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \]
Finally, we multiply this result by 2 to find the surface area:
\[ \text{Surface Area} = 2 \times 725.75 = 1451.5 \text{ in.}^2 \]
Therefore, the surface area of the suitcase is \(1,451.5 \text{ in.}^2\).
So the answer is \(1,451.5 \text{ in.}^2\).