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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.

In this video lesson, you will watch and learn how you can find the area of trapezoid. Learn what measurements you need to have on hand as well as the formula that you need to use.

The formal definition of a **trapezoid** is a four-sided flat shape with one pair of parallel sides. While this gives us the technical specifications of a trapezoid, it doesn't really give us a quick visual. So, one way I describe what a trapezoid looks like is by saying it looks like a triangle with its top cut off. Another way to visualize a trapezoid is by picturing a mountain with straight sides going up and then chopping off the top of the mountain so you have a platform. That will also give you a trapezoid.

In this video lesson, we are going to learn how to find the area of a trapezoid. Before I show you the formula, though, we need to identify the measurements that we will be using.

A trapezoid has two bases, the sides that are parallel to each other. We will label the shorter base *b* and the longer base *a*. A trapezoid also has two legs, the sides that connect the parallel bases. These we aren't going to label. The other measurement that we are going to label is the height, or altitude, of the trapezoid. This we will label *h*. This is the measurement of how tall the trapezoid is when it's sitting flat with the longest base on the floor.

We have labeled the bases with *a* and *b* and the altitude with *h* for a reason. We did this so that we can easily match these measurements up with the formula. The formula uses these letters to identify the measurements that are needed.

Area = ((*a* + *b*)/2) * *h*

Looking at our formula, we see that it is asking us to add the two bases together and then divide that sum by 2. We then take what that equals and multiply it by the altitude or height of the trapezoid to get our area. Seems simple enough, doesn't it? Do your best to memorize this formula. It will serve you well when you need to take a test.

Let's see how this works with an example.

Let's say we are given a trapezoid with bases that measure 8 inches and 5 inches respectively. We are also given the altitude of the trapezoid as 3 inches. The problem didn't give us the length of the legs, but since we want to find the area of the trapezoid, we don't need to know that information, and it's not important.

We have all the information we need; we just need to plug the proper information into the proper location in the formula. Remember the trapezoid we labeled earlier? The longest base is *a*, so my *a* = 8 inches. My other base is 5 inches, so that means my *b* = 5 inches. The altitude is labeled *h*, so my *h* = 3 inches. Now I can plug these numbers into my formula and solve. Let's see what we get.

Area = ((8 + 5)/2) * 3

Area = (13/2) * 3

Area = 6.5 * 3

Area = 19.5 inches squared

So, our answer is 19.5 inches squared. I like using formulas because all I need to do is plug the right numbers in, and I can get my answer. Isn't this process fairly straightforward?

One thing I want to bring to your attention here is that your answer needs to end with your measuring units squared. Do you see how we are using inches and our answer for area is inches squared? If you were measuring in meters, your answer for area needs to be meters squared. Make sure you remember this.

Finding the area of a trapezoid is fairly straightforward with the use of the formula. Let's review what we have learned.

We've learned that a **trapezoid** is formally defined as a four-sided flat shape with one pair of parallel sides. In visual terms, it looks like a triangle or a mountain with a flat platform on top instead of a tip. The formula to find the area of trapezoid is area = ((*a* + *b*)/2) * *h*, where *a* and *b* are the bases (the two parallel sides), and *h* is the altitude or height of the trapezoid. To use this formula, we simply plug in the appropriate measurements where they are needed and evaluate to find the area.

After completing this lesson, you should be able to:

- Define trapezoid
- Identify the formula for finding the area of a trapezoid
- Understand how to label the appropriate measurements used in the formula

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10 in chapter 8 of the course:

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Geometry: High School15 chapters | 160 lessons

- Parallelograms: Definition, Properties, and Proof Theorems 5:20
- Measuring the Area of a Parallelogram: Formula & Examples 4:02
- What Is a Rhombus? - Definition and Properties 4:24
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- Kites in Geometry: Definition and Properties 4:21
- Rectangles: Definition, Properties & Construction 4:08
- Measuring the Area of a Rectangle: Formula & Examples 4:40
- Squares: Definition and Properties 6:52
- Trapezoids: Definition and Properties 4:24
- Measuring the Area of a Trapezoid 4:38
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