Area of a trapezoid (trapezium): formula, calculator and worked example

What the symbols mean

$A$: the area
$a$: one of the parallel sides
$b$: the other parallel side
$h$: the perpendicular height: the distance between the parallel sides

When to use it

Use it for any four-sided shape with one pair of parallel sides (a trapezoid in American English, a trapezium in British English): a cross-section of a ditch or a dam, a field with one slanted edge, a lampshade panel. The same idea, averaging two parallel edges, is the trapezium rule for estimating areas under curves.

Worked example

A garden bed is a trapezoid with parallel sides 6 m and 10 m, 4 m apart. What is its area? (a = 6, b = 10, h = 4)

Start from the formula.
$A = \frac{a + b}{2} h$
Substitute $a$ = $6$ , $b$ = $10$ , $h$ = $4$ and work it out.
$A = \frac{6 + 10}{2} \cdot 4$
$= \frac{16}{2} \cdot 4$
$= 8 \cdot 4$
$= 32$

Answer A = 32 m²

Why it works

Two copies of the trapezoid, one turned upside down, fit together into a parallelogram with base $a + b$ and height h; the trapezoid is half of it. Equivalently, the midline halfway up has length $(a + b)/2$ , the average width.

Common mistakes

Using a slanted side as h. The height is measured at right angles to the parallel sides.
Adding all four sides. Only the two parallel sides go in the bracket.
Forgetting to halve: $(a + b)h$ is twice the area.

Area of a trapezoid (trapezium)

Calculator

See it move

What the symbols mean

When to use it

Worked example

Why it works

Common mistakes