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Median of a Trapezoid: Definition & Theorem

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  • 0:05 Trapezoid Review
  • 1:05 The Median of a Trapezoid
  • 2:05 Finding the Median
  • 3:25 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth Foster

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

If you've ever crossed a bridge, you've probably relied on trapezoids in real life! In this lesson, you'll learn what the median of a trapezoid is, and how to figure out how long it is.

Trapezoid Review

Imagine you're an engineer and you're in charge of building a bridge. The bridge is going to look like this. You can see that the actual bridge is enclosed in a kind of metal cage that holds it up. The cage is longer on the bottom than on the top and it has slanted sides. Let's say the top of the bridge is 500 feet and the bottom of the bridge is 750 feet. You want to build an extra support beam where the purple line is, like this.

Trapezoid bridge
Trapezoid-Bridge-Median

Do you know how long you would need to make the support beam? Well, after this lesson, you will! Let's start with a little geometry: the shape of that bridge is called a trapezoid. A trapezoid is a four-sided shape with at least one pair of parallel sides. The parallel sides can be any two sides. The two parallel sides are called the bases, and the non two-parallel sides are called the legs. Trapezoids have all kinds of properties, but in this lesson, we'll be learning about the median.

The Median of a Trapezoid

The median of a trapezoid is a line parallel to the bases that stretch from the midpoint of one leg to the midpoint of the other. Here, the purple line is the median. This is the same line that represents the support beam on our imaginary bridge; the support beam is the median of the trapezoid. You can see how it cuts each leg in half; the part of the leg above the median is the same length as the part of the leg below the median. The two blue pieces are equal to each other and the two red pieces are equal to each other.

Median of a Trapezoid
Median

This doesn't necessarily mean that the blue pieces are equal to the red pieces. The legs don't have to be exactly the same length. For example, say the red leg is 7 units long, and the blue leg is 8 units long. Then you get this. This is still a median, because both of the blue sections are equal to each other and both of the red sections are equal to each other.

Finding the Median

Many math problems will ask you to find the median of a trapezoid. To do this, you can use a simple formula: the median is the average of the bases. For example, let's say that the top base of our trapezoid is 10 units long and the bottom base is 18 units long. In that case, the median would be the average of 10 and 18.

Remember that the average of a group of numbers is the sum of all the numbers divided by the number of numbers. To find the average, you add up all the numbers and divide by however many numbers you have. In this case, you have two numbers, 10 and 18, so you'd take (10 + 18) / 2. That gives you 28 / 2 or 14 as the average. The length of the median in this trapezoid would be 14.

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