Area of a trapezoid. Definition and formula

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.

(If there is no image below, see support page.)

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

Calculator

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. Since the median of a trapezoid is also the average length of the two bases, the area is also the altitude times the median length.

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:

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)

Try this

In the figure above, click on "hide details"
Drag the orange dots on the vertices to make a random-size trapezoid.
Now try to estimate the area of the trapezoid just looking at the squares inside it

When you done click "show details" to see how close you got.

Coordinate Geometry

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons