Question

A shoe box measures 15 in by 7 in by 4 1/2 in. What is the surface area of the box

Answer 1

408
`in^(2)`

Explanation:

The method that we are going to use in this problem is using nets to find the surface area. In this method we picture the box being cut in different areas to make one large piece of the box (Refer to Image 1).

After we open up the box we can then solve for the surface area of the larger area. (Refer to Image 2)

Since we have the measurements of each area, we solve it like so.

First we add the total length of the cut up box.

4 1/2 + 15 + 4 1/2 + 15 = 39 inches

Now we also know that the width of the box is 7 inches. We just simply multiple both the length of the width together.

7 x 39 = 273
`in^(2)`

Now that we have the value of the larger area of the box, we can then proceed to find the value of one of the extra flaps.

15 x 4 1/2 = 67.5
`in^(2)`

Now that we solved for one side, we can assume that the other side will have the same surface area as they have the same values.

67.5 x 2 = 135
`in^(2)`

Now we simply add up the larger area to the value of the two smaller areas and we end up with our answer.

273 + 135 = 408
`in^(2)`