What this calculator does
A trapezoid has exactly one pair of parallel sides, called the bases, connected by two legs that need not be equal or parallel to each other. The area depends only on the two bases and the perpendicular height between them: the legs affect the shape but not the area.
That last point trips people up. Two trapezoids can share the same bases and height, so the same area, while having completely different legs and looking nothing alike side by side.
The formula
The area formula averages the two parallel sides and multiplies by the height, which is the same as saying the trapezoid has the area of a rectangle whose width equals the median: the line joining the midpoints of the two legs, exactly halfway between the bases in length.
| Term | Meaning |
|---|---|
| a, b | The two parallel sides, or bases. |
| h | The perpendicular height between the two bases. |
| c, d | The two legs, connecting the bases. Need not be equal. |
| Median | The line halfway between the bases, equal to (a + b) ÷ 2. |
The inputs explained
| Field | What to enter |
|---|---|
| Parallel side a | One parallel side. |
| Parallel side b | The other parallel side. |
| Height | The perpendicular distance between the two parallel sides, not the length of a leg. |
| Leg c | One leg, connecting the ends of a and b. |
| Leg d | The other leg. |
When to use it
A sloped garden bed or retaining wall
The face of a bed that is wider at the front than the back is a trapezoid. The area from the two widths and the depth gives the soil or paving needed.
A trapezium-shaped block of land
Many suburban blocks taper along one boundary. Treating the front and back widths as the two bases gives the area without needing the diagonal legs at all.
Cross-sections of drains, canals and hoppers
A trapezoidal channel is a standard shape in civil work because it is stable to excavate and hydraulically efficient: the area here gives the flow cross-section.
Fabric or sheet material cut on an angle
A panel that tapers from one width to another, such as a lampshade side or a skirt panel, is a trapezoid, and the median is the average width used for material estimates.
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 area scales with height, bases fixed at 10 and 6
The two parallel sides held constant while the height between them increases.
| Height | Area | Median (mid-line) |
|---|---|---|
| 2 | 16.000 | 8.000 |
| 4 | 32.000 | 8.000 |
| 5 | 40.000 | 8.000 |
| 8 | 64.000 | 8.000 |
| 10 | 80.000 | 8.000 |
| 15 | 120.000 | 8.000 |
How area changes as the top base widens
One base and the height held fixed while the other base grows from much narrower to equal to the first.
| Other base | Area | Median (mid-line) | Perimeter |
|---|---|---|---|
| 2 | 30.000 | 6.000 | 22.800 |
| 4 | 35.000 | 7.000 | 24.800 |
| 6 | 40.000 | 8.000 | 26.800 |
| 8 | 45.000 | 9.000 | 28.800 |
| 10 | 50.000 | 10.000 | 30.800 |
| 14 | 60.000 | 12.000 | 34.800 |
Questions
What makes a shape a trapezoid rather than a parallelogram?
A trapezoid has exactly one pair of parallel sides. A parallelogram has two pairs, which is the special case where both bases in this calculator are equal.
Do the two legs need to be equal?
No. Equal legs make an isosceles trapezoid, which looks symmetrical, but the area formula works identically whether the legs match or not: it never uses the legs at all.
How is the median different from the average of the bases?
It is not: the median is defined as exactly the average of the two parallel sides, (a + b) ÷ 2. The name refers to its position, halfway between the bases geometrically.
Why doesn’t the area formula use the legs?
Because area only depends on the bases and the perpendicular height between them. The legs can be stretched or skewed, changing the perimeter, without changing the enclosed area as long as the height stays the same.
How do I measure the height if the trapezoid is tilted?
The height must be perpendicular to both parallel sides, not measured along a leg. On a physical object, use a set square or a plumb line from one base to the other rather than a leg length.
For a four-sided shape with two pairs of parallel sides, see the parallelogram calculator. For a shape with no parallel sides, use the triangle calculator after splitting it into triangles.