Measuring the Area of a Trapezoid

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  • 0:06 A Trapezoid
  • 0:38 Identifying Measurements
  • 1:20 The Formula
  • 2:06 Calculating the Area
  • 3:45 Lesson Summary
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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.

A Trapezoid

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.

Identifying Measurements

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.

These are the measurements needed to find the area of a trapezoid.
trapezoid with labeled sides

The Formula

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.

Calculating the Area

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

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