Question

A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?





(1 point)
Responses

96 in.2
96 in.2

1,451.5 in.2
1,451.5 in.2

3,420 in.2
3,420 in.2

725.75 in.2

Answer 1

To find 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,
- \(h\) is the height.

Given:
- Length (\(l\)) = 9.5 inches
- Width (\(w\)) = 16 inches
- Height (\(h\)) = 22.5 inches

Now we can calculate the surface area:

1. First, calculate each of the areas:
- \(lw = 9.5 \times 16 = 152\) square inches
- \(lh = 9.5 \times 22.5 = 213.75\) square inches
- \(wh = 16 \times 22.5 = 360\) square inches

2. Now sum these areas:
\[
lw + lh + wh = 152 + 213.75 + 360 = 725.75 \text{ square inches}
\]

3. Finally, multiply by 2 to get the surface area:
\[
SA = 2(725.75) = 1451.5 \text{ square inches}
\]

So, the surface area of the suitcase is \(1,451.5 \, \text{in}^2\).

**The correct response is: 1,451.5 in.²**