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Median of a trapezoid ("trapezium" in British usage)
 
A line segment between the midpoints of the legs of a trapezoid
Also known as midline or midsegment
Try this Drag the orange dots on each vertex to reshape the trapezoid. Notice the behavior of the red median line.

Properties

The median line is always parallel to the bases. Adjust the trapezoid above by dragging any vertex and convince yourself this is so.

The length of the median is the average length of the bases, or using the formula:

If one of the bases is zero length, the result is a triangle. and is identical to the triangle midsegment case. The median line will then be half the remaining base. Try this out in the figure above by moving A to overlap B.

The median line is halfway between the bases. Adjust the trapezoid above by dragging any vertex and convince yourself this is so.

The median divides the trapezoid into two smaller trapezoids each with half the altitude of the original.

The area of a trapezoid is the altitude × median. See Area of a trapezoid

Things to try

  1. In the figure above, click 'hide details'.
  2. Adjust the points A,B,C,D to create a new trapezoid.
  3. Calculate the length of the median
  4. Click 'show details' to check your answer.
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Other polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons