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, and \( h \) is the height.
Given the dimensions of the suitcase:
- Length \( l = 9.5 \) inches
- Width \( w = 16 \) inches
- Height \( h = 22.5 \) inches
Now, let's calculate each of the areas \( lw \), \( lh \), and \( wh \):
- \( lw = 9.5 \times 16 = 152 \)
- \( lh = 9.5 \times 22.5 = 213.75 \)
- \( wh = 16 \times 22.5 = 360 \)
Now we will sum these areas:
\[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \]
Now, we multiply this sum by 2 to get the total surface area:
\[ \text{Surface Area} = 2 \times 725.75 = 1451.5 \]
So, the surface area of the suitcase is \( 1451.5 , \text{in.}^2 \).
The correct answer is:
1,451.5 in.²