Areas of Parallelograms, Triangles, and Trapezoids
Rule

Area of a Trapezoid

The area of a trapezoid is half the height times the sum of the lengths of the bases. In other words, the area of a trapezoid is the height multiplied by the average of the bases.

Proof

Consider a trapezoid with bases and and height

Trapezoid

Drawing a diagonal divides the trapezoid into two triangles. Therefore, the area of the trapezoid can be written as the sum of the areas of the triangles.

Trapezoid

Take as the base of the upper triangle and draw the corresponding altitude from the opposite vertex.

Trapezoid
Notice that both triangles have the same height, which is the height of the trapezoid. The area of the bottom triangle is half the product of and and the area of the upper triangle is half the product of and
Finally, add these two areas to write a formula for the area of the trapezoid.

Extra

Graphical Derivation
The formula for the area of a trapezoid with bases and and height can be derived by transforming the trapezoid into a triangle with base and height
Converting a trapezoid into a triangle
Exercises