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Calculating the Median of a Trapezoid

Laura Foist, Elizabeth Foster
  • Author
    Laura Foist

    Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

  • Instructor
    Elizabeth Foster

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

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

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What is a Trapezoid?

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

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  • 0:05 Trapezoid Review
  • 1:05 The Median of a Trapezoid
  • 2:05 Finding the Median
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Median of a Trapezoid

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.


Image 1: The median line in a trapezoid cuts the trapezoid into two smaller trapezoids with equal altitudes.

Image of a trapezoid with the median line


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.


Image 2: Even if a trapezoid is drawn with the bases vertical, instead of horizontal, the bases are still the parallel sides, not the horizontal sides, making the median vertical.

Image of a trapezoid with the median line drawn where the bases are vertical


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.

Formula for the Median of a Trapezoid

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.

How to Find the Median of a Trapezoid

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

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Frequently Asked Questions

What is the formula to find the median of a trapezoid?

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

How do you find the median of a trapezoid?

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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