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)

96 in.2

725.75 in.2

1,451.5 in.2

3,420 in.2

Answer 1

To calculate 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, and
- \( h \) is the height.

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

Now, plugging in the values:

\[
SA = 2( (9.5 \times 16) + (9.5 \times 22.5) + (16 \times 22.5) )
\]

Calculating each part:

1. \( 9.5 \times 16 = 152 \)
2. \( 9.5 \times 22.5 = 213.75 \)
3. \( 16 \times 22.5 = 360 \)

Now, adding them together:

\[
152 + 213.75 + 360 = 725.75
\]

Now multiply by 2:

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

Thus, the surface area of the suitcase is:

\[
\boxed{1,451.5 \text{ in}^2}
\]