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?

96 in.2
2
96 in.2

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

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

725.75 in.2

Answer 1

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

Given:
- \( l = 9.5 \) inches,
- \( w = 16 \) inches,
- \( h = 22.5 \) inches.

Now, substitute the 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 \( wh \):
\[
wh = 16 \times 22.5 = 360 \text{ in}^2
\]

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

Finally, multiply by 2 to find the total 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 in²**.