Area of a Trapezoid Calculator
This calculator finds the area of a trapezoid, called a trapezium in New Zealand, Australia and the United Kingdom, a four-sided shape with exactly one pair of parallel sides. You enter the lengths of the two parallel sides, labelled base a and base b, along with the perpendicular height, which is the straight vertical distance between those two sides rather than the length of either slanting leg. Choose a unit of measurement from centimetres, metres, millimetres, kilometres, inches, feet, yards, miles or generic units, and keep all three measurements in that same unit. The calculator applies the standard formula A = (a + b) / 2 x h, taking the average of the two bases and multiplying it by the height. It returns the area in square units, the average of the bases (the midline length), and the sum of the two bases for reference. Full step-by-step working is shown beneath the results so you can follow how the area was reached, alongside a dimensions summary and a note on whether your shape has simplified to a parallelogram, which happens whenever base a and base b are equal. Use this for maths homework, trade measurements or paving and fabric layouts, and take care to measure the perpendicular height rather than a slanted edge, since using the wrong height is the most common source of error.
1. Parallel Sides (Bases)
2. Unit of Measurement
All three values must be in the same unit. The area result is returned in square units of the length you choose (e.g. m gives m²).
Step-by-step working
Dimensions
Notes on Measurement
How to Calculate the Area of a Trapezoid
A trapezoid (called a trapezium in New Zealand, Australia, and the UK) is a four-sided flat shape with exactly one pair of parallel sides. Those parallel sides are called the bases. The perpendicular distance between the two bases is the height.
The area formula is:
A = (a + b) / 2 x h
where a is the length of the first base, b is the length of the second base, and h is the perpendicular height. You can also write this as A = ((a + b) x h) / 2, which means the same thing: find the average of the two bases, then multiply by the height.
Why the Formula Works
One way to see why this formula is correct is to imagine cutting a trapezoid in half horizontally at the midpoint of its height. You get two smaller trapezoids. If you flip one piece upside down and place it next to the other, the two pieces form a parallelogram whose base equals (a + b) and whose height equals h / 2. The area of a parallelogram is base x height, so the area of the two halves combined is (a + b) x (h / 2), which equals (a + b) / 2 x h. That is the same as the trapezoid area formula.
Another way to think about it: the average of the two bases is the length of the midsegment (the line joining the midpoints of the two non-parallel sides). Multiplying the midsegment by the full height gives the area.
Worked Example
A trapezoidal garden bed has a front edge of 6 m, a back edge of 10 m, and a depth (perpendicular distance between front and back) of 4 m. What is the area?
A = (6 + 10) / 2 x 4 = 16 / 2 x 4 = 8 x 4 = 32 m²
This matches the default output of the calculator above.
Common Mistakes
- Using the slant leg instead of the perpendicular height. The formula requires the vertical distance between the two parallel sides, not the length of either angled leg. If you only know the leg length, use the Pythagorean theorem to find h first.
- Mixing units. All three inputs (a, b, and h) must be in the same unit. If one side is in centimetres and another in metres, convert before calculating.
- Confusing which sides are parallel. Only a and b (the two bases) are parallel. The other two sides (the legs) can be any length or angle.
Special Cases
| Shape | Condition | Area formula |
|---|---|---|
| General trapezoid | a not equal to b | A = (a + b) / 2 x h |
| Parallelogram | a = b (both bases equal) | A = a x h (simplifies from formula) |
| Rectangle | a = b and both legs perpendicular | A = a x h |
| Right trapezoid | One leg is perpendicular to both bases | A = (a + b) / 2 x h (same formula) |
| Isosceles trapezoid | Both legs are equal length | A = (a + b) / 2 x h (same formula) |
When a equals b, the shape becomes a parallelogram and the formula simplifies to A = a x h. You can verify this by substituting a = b into (a + b) / 2, which gives (a + a) / 2 = a.
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Sources and method: Formula A = (a + b) / 2 x h is the standard Euclidean geometry result for the area of a trapezoid, derived from the parallelogram area formula. See: Weisstein, Eric W. "Trapezoid." MathWorld (mathworld.wolfram.com/Trapezoid.html). New Zealand Mathematics Curriculum (nzmaths.co.nz), Level 4 Geometry strand.
This calculator computes area from the inputs you provide. Ensure that the height entered is the perpendicular distance between the two parallel sides, not the length of a slant leg. All inputs must share the same unit of measurement.