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. squared 1,451.5 in.2 1 comma 451 point 5 in. squared 3,420 in.2 3 comma 420 in. squared 725.75 in.2 725 point 7 5 in. squared

Answer 1

To find the surface area of a rectangular suitcase, we can use the formula for the surface area \( A \) of a rectangular prism:

\[
A = 2(lw + lh + wh)
\]

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 we can substitute these values into the formula:

1. Calculate \( lw \):

\[
lw = 9.5 \times 16 = 152 \, \text{in}^2
\]

2. Calculate \( lh \):

\[
lh = 9.5 \times 22.5 = 213.75 \, \text{in}^2
\]

3. Calculate \( wh \):

\[
wh = 16 \times 22.5 = 360 \, \text{in}^2
\]

4. Now, add these areas together:

\[
lw + lh + wh = 152 + 213.75 + 360 = 725.75 \, \text{in}^2
\]

5. Finally, multiply by 2 to get the surface area:

\[
A = 2 \times 725.75 = 1451.5 \, \text{in}^2
\]

Thus, the surface area of the suitcase is:

**1,451.5 in.²** (or **1 comma 451 point 5 in. squared**) is the correct response.