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

725.75 in.2
725 point 7 5 in. squared

96 in.2
96 in. squared

3,420 in.2
3 comma 420 in. squared

1,451.5 in.2

Answer 1

To calculate the surface area of a rectangular box (in this case, the suitcase), you can use the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

For the suitcase:
- \( l = 9.5 \) inches
- \( w = 16 \) inches
- \( h = 22.5 \) inches

Now plug in the values:

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

5. Finally, multiply by 2 to get the surface area:
\[
\text{Surface Area} = 2 \times 725.75 = 1451.5 \, \text{in}^2
\]

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