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Area of a trapezoid ("trapezium" in British usage)
 
The number of square units it takes to completely fill a trapezoid.
Formula: Average width × Altitude
Try this Drag the orange dots to move and resize the trapezoid. As the size of the trapezoid changes, the area is recalculated.


Area formula

The area of a trapezoid is given by the formula

 where
b1, b2 are the lengths of the two bases
a is the altitude of the trapezoid 		 

Recall that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases. This is equivalent to the altitude times the average length of the bases.

If you know the median

Recall that the median (m) of a trapezoid is the line segment linking the midpoints of the non-parallel sides. Recall also that the median's length is the average of the two parallel sides. See Median of a Trapezoid

If the median length is m, and the altitude h, the area of the trapezoid is

Area as a compound shape

Another way to find the area of a trapezoid is to treat it as some simpler shapes, and then add or subtract their areas to find the result. For example, a trapezoid could be considered to be a smaller rectangle plus two right triangles: Trapezoid as a compound shape For more on this general technique, see Area of Irregular Polygons.

Coordinate Geometry

In coordinate geometry, if you know the coordinates of the four vertices, you can calculate various properties of it, including the area and perimeter. For more on this, see Trapezoid area and perimeter (Coordinate Geometry)

Area of a Trapezoid videos

Below are four videos of an instructor explaining the concepts and example problems on a white board

Things to try

  1. In the figure above, click on "hide details"
  2. Drag the orange dots on the vertices to make a random-size trapezoid.
  3. Calculate the area using the formula
  4. Now try to estimate the area of the trapezoid just looking at the squares inside it
  5. When you done click "show details" to see how close you got.

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons

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