Learning Center / Geometry

Area of a trapezium (trapezoid): formula and examples

The formula for the area of a trapezium (a trapezoid in the US), why it works, and worked examples — including finding a missing height or side.

2 min readUpdated 2 November 2026By Sumzo team (AI-assisted)Reviewed by Sumzo AI (owner-delegated review)

The area of a trapezium is half the sum of its two parallel sides, multiplied by the perpendicular height between them. A trapezium is a four-sided shape with exactly one pair of parallel sides; in the US it is called a trapezoid, and the formula is the same.

A=12(a+b)hA = \frac{1}{2}(a + b)h
$a$ and $b$ are the parallel sides; $h$ is the perpendicular height between them.

How to find the area of a trapezium

  1. Identify the two parallel sides, aa and bb.
  2. Find the height hh — the perpendicular distance between them, not a slanted side.
  3. Add the parallel sides, multiply by the height, and halve.
  4. Give the answer in square units, such as cm2\text{cm}^2.

Worked example

Easy: whole numbers

A trapezium has parallel sides 6 cm and 10 cm, and height 4 cm. Find its area.

Show the working
  1. Substitute into the formula.
    A=12(6+10)×4A = \tfrac{1}{2}(6 + 10) \times 4
  2. Work it out.
    12×16×4=32\tfrac{1}{2} \times 16 \times 4 = 32

Answer: 32 cm232\text{ cm}^2

Checked by Sumzo’s math engine

Worked example

Medium: decimals

Find the area of a trapezium with parallel sides 7.5 m and 12.5 m and height 6 m.

Show the working
  1. Add the parallel sides.
    7.5+12.5=207.5 + 12.5 = 20
  2. Multiply by the height and halve.
    12×20×6=60\tfrac{1}{2} \times 20 \times 6 = 60

Answer: 60 m260\text{ m}^2

Checked by Sumzo’s math engine

Worked example

Hard: find the height from the area

A trapezium has area 45 cm245\text{ cm}^2 and parallel sides 8 cm and 10 cm. How tall is it?

Show the working
  1. Put the known values into the formula.
    45=12(8+10)h45 = \tfrac{1}{2}(8 + 10)h
  2. Simplify the right side.
    45=9h45 = 9h
  3. Divide by 9.
    h=5h = 5
  4. Check: 12(8+10)×5=45\tfrac{1}{2}(8 + 10) \times 5 = 45 ✓.

Answer: The height is 5 cm.

Checked by Sumzo’s math engine

Why the formula works

Take two copies of the same trapezium and turn one upside down next to the other. Together they make a parallelogram with base a+ba + b and height hh, so its area is (a+b)h(a + b)h. One trapezium is half of that: 12(a+b)h\frac{1}{2}(a + b)h. You can also think of it as the average of the parallel sides, a+b2\frac{a + b}{2}, times the height.

Common mistakes

  • Using a slanted side as the height — the height is perpendicular to the parallel sides.
  • Forgetting the 12\frac{1}{2}.
  • Adding a non-parallel side to a+ba + b.
  • Mixing units, such as one side in mm and the height in cm.

Frequently asked questions

What is the formula for the area of a trapezium?

A=12(a+b)hA = \frac{1}{2}(a + b)h, where aa and bb are the parallel sides and hh is the perpendicular height between them.

Is a trapezium the same as a trapezoid?

In British English a trapezium has one pair of parallel sides; in American English that shape is a trapezoid. The area formula is the same.

How do you find the area of a trapezium without the height?

Work out the height first. Usually you can draw it in to form a right triangle with a slanted side and use Pythagoras’ theorem.

Calculators

Practice

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