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

1,451.5 in.2

3,420 in.2

725.75 in.2

Answer 1

To find the surface area of the suitcase, which has the dimensions:

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

The formula for the surface area \( A \) of a rectangular prism is:

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

Now, we will calculate each of the products:

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

Now we sum these products:

\[
lw + lh + wh = 152 + 213.75 + 360 = 725.75
\]

Now we multiply by 2 to find the surface area:

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

Therefore, the surface area of the suitcase is:

**1,451.5 in.²**