Surface Area of Rectangular Prisms Educational Resources K12 Learning, Geometry, Math Lesson Plans, Activities, Experiments, Homeschool Help

Lesson Plan - Get It!

Audio:

Imagine you are going to your best friend's birthday party.

You order your friend's gift online, and it arrives in a box like this:

package

For the birthday party, you want to wrap the box in your friend's favorite color: blue!

wrapping paper

There's not much paper left on the roll.

Will you have enough to wrap the box?
How can you find the answer to this question?

You could grab your scissors and tape and just start cutting the wrapping paper, taking a chance that there is enough.

Or, you can calculate the surface area of the box!

A box like this is a three-dimensional shape and is called a rectangular prism. If you need to review three-dimensional shapes, visit the Related Lessons found in the right-hand sidebar.

Let's quickly sketch the box. Pay attention to what is labeled as the length, width, and height:

surface area example 1

Now, let's look at the measurements of the length, width, and height of the box:

surface area example 2

There are two ways to find the surface area of a rectangular prism:

Find the area of all six sides, and then add the areas together to find the surface area.
Use a formula.

First, let's try the add the areas together method.

You will need to add the area of all six sides:

Side 1 + Side 2 + Side 3 + Side 4 +Side 5 + Side 6

Look at the yellow highlighted side of the rectangular prism:

surface area example 3

This shape is a two-dimensional rectangle. To find the area, you will multiply the two sides:

surface area example 4

If you need to review finding the area of a rectangle, visit the area lesson in Related Lessons.

This same rectangle is on two sides of this rectangular prism. Therefore, we already know the area for two sides:

35 + 35 + Side 3 + Side 4 + Side 5 + Side 6

Now, let's find the area of the other two sides:

surface area example 5

This same rectangle is on both ends of the rectangular prism:

35 + 35 + 20 + 20 + Side 5 + Side 6

Now, let's find the area of the last two sides:

surface area example 6

We finally know the areas of all six sides of the rectangular prism:

35 + 35 + 20 + 20 + 28 + 28

If you add all the areas together, you will end up with the surface area of the box!

166 inches squared

Great!

Now, let's try to find the surface area again. This time we will use the formula method!

Surface Area of a Rectangular Prism = 2(WL + HL + HW)

Look at the measurements of the box again:

surface area example 7

Now, use the formula and the measurements to calculate the surface area:

surface area example 8

Using both methods, we found that the surface area of the box is 166 inches squared!

This means we will need at least 166 square inches of wrapping paper to cover the box!

We will figure out if there is enough paper later. But first, visit the Got It? section to practice finding the surface area of more rectangular prisms!