What this calculator does
A trapezium (called a trapezoid in the US) has one pair of parallel sides and one pair that are not. The area of trapezium depends only on the lengths of those two parallel sides and the perpendicular height between them; the two non-parallel legs do not affect the area at all.
This calculator asks only for what the formula actually needs: the two parallel sides and the height, nothing more. That keeps it a genuinely quick way to find the area of a trapezium, without measuring legs that turn out not to matter for this particular question.
The formula
The trapezium area formula is area = ½ × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the perpendicular height between them. It is the same idea as averaging the two parallel sides into a single "mean width" and multiplying by the height.
| Term | Meaning |
|---|---|
| a, b | The two parallel sides of the trapezium. |
| h | Height: the perpendicular distance between the two parallel sides. |
| Median | The average of the two parallel sides, (a + b) / 2, equal to the length of the mid-line joining the non-parallel sides. |
The inputs explained
| Field | What to enter |
|---|---|
| Parallel side a | The length of one parallel side. |
| Parallel side b | The length of the other parallel side. |
| Height (perpendicular distance between the parallel sides) | The perpendicular height between the two parallel sides, not the length of a slanted leg. |
When to use it
A trapezium-shaped plot of land or panel
A block of land, a roof panel or a fabric cut that is wider at one end than the other is a common real-world trapezium, and the area of trapezium formula gives its area directly from a survey or measured drawing.
Cross-sections in engineering and earthworks
The cross-section of a canal, drain or embankment is often a trapezium in profile; its area, multiplied by length, gives the volume of material to excavate or fill.
Checking a formula from a maths problem
How to find the area of a trapezium is a common school geometry question; entering the two parallel sides and the height here checks a hand-worked answer.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How to find the area of a trapezium as one parallel side changes
A fixed second parallel side of 6 and height of 5, across a range of values for the first parallel side.
| Parallel side a | Area | Median (average of the two parallel sides) |
|---|---|---|
| 4 | 25.000 | 5.000 |
| 6 | 30.000 | 6.000 |
| 8 | 35.000 | 7.000 |
| 10 | 40.000 | 8.000 |
| 14 | 50.000 | 10.000 |
| 20 | 65.000 | 13.000 |
Trapezium area formula: how height affects the area
Fixed parallel sides of 10 and 6, across a range of height values.
Questions
What is the area of trapezium formula?
Area = ½ × (a + b) × h, where a and b are the two parallel sides and h is the perpendicular height between them.
How do you find the area of a trapezium without the height?
You cannot use this formula without a height; if only the four side lengths are known, the height must first be worked out from the legs and the difference between the parallel sides using the Pythagorean theorem.
Do the two non-parallel legs affect trapezium area?
No. Area of trapezium depends only on the two parallel sides and the perpendicular height between them; the legs affect the perimeter and the shape’s slant, but not the enclosed area.
What is the difference between a trapezium and a trapezoid?
They are the same shape under two different names. British English calls a quadrilateral with one pair of parallel sides a trapezium; American English calls it a trapezoid, and reserves "trapezium" for a shape with no parallel sides at all.
For the perimeter as well, including both non-parallel legs, see the full trapezoid calculator. For a four-sided shape with two pairs of parallel sides instead, see the parallelogram & rhombus calculator.