Area of a Trapezoid

Area of a Trapezoid

How to find the area of a trapezoid: formula, proof, example, and its solution.

Formula

A = (1/2)(b1 + b2)h. A: area of a trapezoid. b1, b2: base. h: height.

A = (1/2)(b1 + b2)h

A: area of a trapezoid
b1, b2: bases
h: height

Proof

Area of a Trapezoid: Proof of the Formula

By a diagonal,
a trapezoid is divided into two triangles.

The areas of the triangles are (1/2)b1h and (1/2)b2h.

So A = (1/2)b1h + (1/2)b2h
= (1/2)(b1 + b2)h

Example

Find the area of the given trapezoid. Bases: 5, 8. Height: 4.

b1 = 5, b2 = 8, h = 4

A = (1/2)(5 + 8)⋅4