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:

$SAt=SA1+SA2+SA3\\SAt=3,664in^{2}+1,350in^{2}+600in^{2}\\SAt=5,614in^{2}$