Question

For your friend's birthday, you have 3 presents to wrap. Find the combined surface area of these 3 gifts so you know how much wrapping paper you will need.

Answer 1

The answer is: 5,614 square inches.

The explanation is shown below:

1. The gift on the bottom is a rectangular prism. To calculate its surface area, you must apply the following formula:

`SA=2[(l)(w)+(l)(h)+(h)(w)]`

Where
`l` is the length (20 inches),
`w` is the width (42 inches) and
`h` is the heigth (16 inches).

2. Substitute values:

`SA1=2[(20in)(42in)+(20in)(16in)+(16in)(42in)]=3,664in^{2`

3. The surface area of the other gifts can be calculated with the formula for calculate the surface area of a cube:

`SA=6s^(2)`

Where
`s` is the side.

4. The surface area of the bigger cube is:

`SA2=6(15in^(2))=1,350in^(2)`

5. The surface area of the smaller cube is:

`SA3=6(10in^(2))=600in^(2)`

6. The total surface area (the combined surface area of the three gifts) is:

`SAt=SA1+SA2+SA3\\SAt=3,664in^(2)+1,350in^(2)+600in^(2)\\SAt=5,614in^(2)`