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? *Hint: Don't forget to use your Desmos calculator and STAAR Reference Sheet to help! (1 point) Responses 96 in.2 96 in.2 1,451.5 in.2 1,451.5 in.2 3,420 in.2 3,420 in.2 725.75 in.2 725.75 in.2 Skip to navigation

Answer 1

To find the surface area of a rectangular suitcase, you can use the formula for the surface area \( S \) of a rectangular prism:

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

where:

• \( l \) = length
• \( w \) = width
• \( h \) = height

Given the dimensions:

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

Now, let's calculate the area:

1. Calculate each of the products:

   • \( lw = 9.5 \times 16 = 152 \)
   • \( lh = 9.5 \times 22.5 = 213.75 \)
   • \( wh = 16 \times 22.5 = 360 \)

2. Add these products together: \[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \]

3. Multiply by 2 to find the surface area: \[ S = 2 \times 725.75 = 1451.5 \text{ in}^2 \]

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

The correct response is 1,451.5 in.².