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

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

96 in.2
96 in. squared

1,451.5 in.2
1 comma 451 point 5 in. squared

725.75 in.2

1 answer

To find the surface area of a rectangular 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, and \( h \) is the height.

Given the dimensions of the suitcase:

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

Now, let's calculate each of the areas \( lw \), \( lh \), and \( wh \):

  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 will sum these areas:

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

Now, we multiply this sum by 2 to get the total surface area:

\[ \text{Surface Area} = 2 \times 725.75 = 1451.5 \]

So, the surface area of the suitcase is \( 1451.5 , \text{in.}^2 \).

The correct answer is:

1,451.5 in.²