## Table of Contents

- What is a Trapezoid?
- Median of a Trapezoid
- Formula for the Median of a Trapezoid
- How to Find the Median of a Trapezoid
- Median of a Trapezoid Examples
- Lesson Summary

Learn what a trapezoid is and how to define the median of a trapezoid. Discover the formula for the median of a trapezoid and examples of when it is used.
Updated: 06/28/2022

- What is a Trapezoid?
- Median of a Trapezoid
- Formula for the Median of a Trapezoid
- How to Find the Median of a Trapezoid
- Median of a Trapezoid Examples
- Lesson Summary

A **trapezoid** is a quadrilateral (or a shape with four sides) where only two of the sides are parallel. The two parallel sides are called **bases** and the two non-parallel sides are **legs**. There are several different types of trapezoids, including:

- Scalene: none of the sides are equal in length
- Isosceles: The legs are equal in length
- Acute: two angles that are adjacent to each other have angles of less than 90 degrees
- Obtuse: two angles that are opposite each other have angles of more than 90 degrees
- Right: two angles that are adjacent to each other are 90 degrees

One line that is used to describe and measure a trapezoid is the median. What is the median of a trapezoid? The **median** of a trapezoid is a line connecting the two legs' midpoints. The midpoint is the point on the leg that cuts that leg in half. The median is always parallel to the bases and falls halfway between the two bases. The length is the average length of the two bases. It creates two smaller trapezoids, each having the same altitude (height), but not necessarily the same area.

The median is an important measurement because the area of a trapezoid is equal to the median times the altitude. So, to find the area of a trapezoid the median first needs to be found.

In image 1 of a trapezoid, sides a and b are the bases and line m is the median. The two single dash lines on the left leg indicate that each segment is equal in length, showing that the median meets at the midpoint of the leg. The two double dash lines on the right leg indicate that each segment of that leg is also equal in length, showing that the median meets at the midpoint of that leg as well.

The important aspect of the median is that it creates two equal segments between the legs and is parallel to the bases, it is not always a horizontal line. If the trapezoid is drawn with the bases vertical and the legs horizontal, then the median will be vertical, instead of horizontal, as seen in image 2.

It is important to find the length of the median of the trapezoid to calculate the area of the trapezoid. The length of the median is equal to the average length of each base. This means that the median of a trapezoid formula is {eq}\frac{a+b}{2} {/eq} this could also be written as {eq}\frac{1}{2} (a+b) {/eq}. Where a is the length of the base a and b is the length of base b. This formula calculates the average length of each base and the length of the median.

The median of a trapezoid formula can be used to find the median. The following steps will show how to find the median of the trapezoid:

- Find the length of base a
- Find the length of base b
- Add the length of base a plus base b
- Divide the resulting sum by 2

To find the length of the bases check the diagram given and be sure the lengths used are the bases, not the legs. A base will always have another line that is parallel to it. If there is no line that is parallel to it, then it is a leg instead of a base. Both lengths will be a positive number, and it does not matter which order the bases are added together. Base a can be added to base b, or base b can be added to base a. Ensure that the units of each base are the same.

The median of the following trapezoids can be found as seen in image 3.

To find the median of trapezoid ABCD, first list the lengths of the bases:

- Base a is side AB: 2
- Base b is side CD: 4

Add the two bases: {eq}2+4=6 {/eq}

Divide the sum by two: {eq}\frac{6}{2}=3 {/eq}

The median of trapezoid ABCD is 3.

To find the median of trapezoid EFGH, first list the lengths of the bases:

- Base a is side EF: 2
- Base b is side GH: 6

Add the two bases: {eq}2+6=8 {/eq}

Divide the sum by two: {eq}\frac{8}{2}=4 {/eq}

The median of trapezoid EFGH is 4.

To find the median of trapezoid IJKL, first list the lengths of the bases:

- Base a is side IJ: 3
- Base b is side KL: 5

Add the two bases: {eq}3+5=8 {/eq}

Divide the sum by two: {eq}8 \div 2=4 {/eq}

The median of trapezoid IJKL is 4.

The formula can also be rearranged to find the base of a trapezoid if the median and one base are known. The length of a base can be calculated using the formula: {eq}a=2m-b {/eq}

The trapezoid in image 7 has a length of m, or the median equal to 6. And the length of base b (of side TU) is equal to 4. This information can be plugged into the formula: {eq}a=(2 \times 6) - 4 = 12 -4 = 8 {/eq}. The length of base TU is 8 units.

A **trapezoid** is a shape with four sides, where only two of the sides are parallel. The **legs** are the two non-parallel sides, and the **bases** are the two parallel sides. If each leg is split into two equal segments the line between those two points is the **median**. The median is also parallel to the two bases, and it is the average length of the two bases. The formula to find the median is: {eq}m=\frac{a+b}{2} {/eq}, where a and b are the lengths of the bases. The formula can also be rearranged to find the length of a base: {eq}a=2m-b {/eq}.

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Frequently Asked Questions

The formula to find the median of a trapezoid is (a+b)/2. Where a and b are the lengths of each base.

The median of a trapezoid is equal to the average of the two bases. This is found by adding each base together and then dividing the sum by 2.

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