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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Look around you, and you see rectangles all over the place. And if you see paint, carpet, or anything that covers a rectangular area, you can be sure that someone has measured the area of the rectangle. Watch this video lesson to learn more.

Rectangles are important. Just look around, and what do you see? Tons of rectangles everywhere! If you're looking at a computer screen, what do you see right now? Don't you see a rectangle? How can you be sure that you're looking at a rectangle? Well, by definition, a **rectangle** is a four-sided shape whose angles are all right angles measuring 90 degrees. So, if you see a shape with four sides and four right angles, then you can be sure that you're looking at a rectangle.

One important calculation you can do with rectangles is to find their area. Why is this important? Is the room you are in rectangular in shape? What about the wall you're staring at? Is that rectangular in shape? If so, what do you see covering the floor or the wall? Do you see paint or carpet or tile of some sort? If you do, then the formula for the rectangle's area was used to figure out how much paint and floor covering was needed.

The formula they used is a simple one. It is area = length * width. Yes, the formula is simply the multiplication of one side with its neighboring side. It doesn't matter which side you pick to be the length. Whatever side you pick, the side next to it will be the width. The remaining two sides will have the same measurement as the side they are opposite to. Typically, in a rectangle, one side is longer than the other. If the longer side is your length, then make your shorter side your width. You can also choose your longer side to be the width, which will make your shorter side the length.

Let's see how we can put this formula into use. We'll start with a plain rectangle just to see how the numbers work with each other. This particular rectangle we are looking at below has a length of 5 feet and a width of 3 feet. So, what do you think we need to do with these two numbers in order to find our area? That's right - we are going to multiply the two numbers together. When we do that, we get 5 feet * 3 feet = 15 feet squared. Notice how my answer has our measuring unit squared. That is because I have multiplied two numbers that have units. Just remember, your answer for area will always end with your measuring unit squared.

Now that we know how to use the formula with a plain rectangle, let's see what's it's like to use it in a real-world project. Pretend that you are the chief carpet layer for a carpet company. You just received a job that requires you to find out how much carpet is needed to get a job done. The only thing you are given is a measuring tape. What do you do?

First, you look around the room that needs to be carpeted and check to make sure it is a rectangle. You see four walls and four corners that are right angles. Everything checks out. The room is rectangular. Then, you pick one side of the room to measure. You find that this side measures 12 feet.

Okay - so far, so good. Then you measure the side next to the side you just measured and find that it measures 10 feet. That's all the measurements you need. One will be the length and the other the width. If the 12-foot side is the length, then the 10-foot side is the width. Now that the two measurements are labeled, they are ready to be used in the formula.

Plugging the two numbers in, you find that the area of the room is 12 feet * 10 feet = 120 feet squared. So, that means you need 120 square feet of carpet to do the job. You report back to your company, and the client gets her carpet laid with just the right amount of carpet for the job and with no waste.

What can we say about rectangles now? We can say that **rectangles** are four-sided shapes whose angles are all right angles measuring 90 degrees. We can also say that the formula to find the area of a rectangle is area = length * width. To use the formula, all you need to know is the measurements of the sides of a rectangle. We pick one side as the length, and the other side next to it is the width. We just plug these two numbers into the formula, and we can find the area. In the real world, it is used to find how much flooring is needed to cover a rectangular room and likewise with paint to cover a rectangular wall.

By finishing this lesson, you could develop the ability to:

- Explain what constitutes a rectangle
- Understand the process of calculating square footage
- Implement the formula for finding the area of a rectangle

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Geometry: High School15 chapters | 160 lessons

- Parallelograms: Definition, Properties, and Proof Theorems 5:20
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- Trapezoids: Definition and Properties 4:24
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- Using Heron's Formula in Geometry 5:54
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