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)
96 in.
2
1,451.5 in.
2
3,420 in.
2
725.75 in.
2

1 answer

To calculate the surface area of the suitcase, which is a rectangular prism, 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:

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

First, we 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:

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

Finally, we multiply this result by 2 to find the surface area:

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

Therefore, the surface area of the suitcase is \(1,451.5 \text{ in.}^2\).

So the answer is \(1,451.5 \text{ in.}^2\).