*Elizabeth Foster*Show bio

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Lesson Transcript

Instructor:
*Elizabeth Foster*
Show bio

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Understanding how to calculate area is valuable to real-world situations like decorating a room or plotting a garden. Learn how geometry and area are applied in the real world, and see example problems using carpet and trampoline installation and mowing the lawn.
Updated: 11/18/2021

In this lesson, we're going to go over some real-world applications of area. But first, we'll get a quick refresher on what area is and how to calculate it.

**Area** is the amount of space covered by a two-dimensional shape.

To find the area of a square or rectangle, multiply the length times the width. To find the area of a circle, multiply pi times the radius squared. To find the area of a triangle, multiply one-half the base times the height. If you want to find the area of a more complicated shape, start by breaking it up into smaller parts.

Now, let's look at some real-world problems involving area.

*Sue is getting new carpet for her house. She can choose between two carpet installers. One will install any amount of carpet for a flat fee of $100. The other charges $0.85 per square foot. Sue's living room is 10 feet long and 14 feet wide. Which carpet installer should she choose?*

Well, first we'll have to figure out how many square feet of carpet she needs, so we can tell what Installer B charges. Sue's living room is 10 feet long and 14 feet wide, so the area is

10 * 14 = 140 square feet

At $0.85 per square foot, that's $119 to install. So, Sue would be better-off going with the flat fee of $100, which would save her $19.

Saving $19 might not be huge money, but it would probably be appreciated by the hard-working protagonist of our next problem. Here it is:

*Mark's mother pays him to mow the lawn. Their lawn looks like this (see video). If Mark makes $0.05 per square foot of lawn, how many times will he have to mow the lawn to pay the $56 he needs to fill up his gas tank?*

You can see here that the lawn is basically a rectangle with a triangle stuck onto it at the end. The length of the rectangle is 20 feet, and the width is 8 feet. So, the area of just the rectangle part is

20 * 8 = 160 square feet

The width of the rectangle is also the base of the triangle. The height of the triangle is 10 feet. So, the area of the triangular part is

1/2 * 8 * 10 = 40 feet

40 + 160 is 200, so the entire area of the lawn is 200 feet. At $0.05 per square foot, that's $10 for mowing the lawn. To fill his tank, Mark would have to mow the lawn 6 times. At least it's a pretty small lawn!

A small lawn might be easy for Mark to mow, but it's not so wonderful for the next problem, which is all about how much stuff you can cram into the backyard.

*Johan loves trampolines, and he wants to buy the biggest trampoline that will fit in his yard. All of his trampoline options are circular. He has his choice of three sizes:*

*Mega Bounce: 200 square feet of bouncing area**Super Bounce: 150 square feet of bouncing area**Budget Bounce: 110 square feet of bouncing area*

*Johan's yard is 15 feet long by 18 feet wide. How big a trampoline can he fit?*

Here, you're given the area of three circles, and you need to backtrack to find the radii, to see which trampoline will fit in Johan's yard.

*a* = pi * *r*^2

Plugging the three areas into this equation, we get:

Radius of the Mega Bounce: roughly 8 feet

Radius of the Super Bounce: roughly 7 feet

Radius of the Budget Bounce: roughly 6 feet

That means the diameters of the trampolines are 16, 14, and 12 feet, respectively. So Johan's yard can hold the Super Bounce, but it's too small for the Mega Bounce, because it's only 15 feet long. The biggest trampoline Johan can buy is the Super Bounce.

In this lesson, you worked through some problems about using area in real-world situations.

First, we saved some money on carpet by figuring out that the flat rate was actually cheaper than the per-foot rate for installation. Next, we found out how many times poor Mark has to mow the lawn before he can fill up his gas tank. In this problem, you saw how helpful it is to break down big shapes into smaller ones. And finally, we calculated just how big a trampoline Johan can fit onto his lawn. Remember, to find the area of a square or rectangle multiply the length times the width. To find the area of a circle, multiply pi times the radius squared. To find the area of a triangle, multiply one-half the base times the height.

Now, try your hand at the quiz questions!

After reviewing this lesson, you should be able to:

- Define the area of a shape
- Demonstrate how to find the area of a shape

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