Guide
How to use Trapezoid Area Calculator
Start with the working tool above. The notes below explain the inputs, method, limitations and checks that matter for this specific task.
- 1. Measure the two parallel sides of the shape; call them a and b.
- 2. Measure the height: the straight, perpendicular distance between those two sides.
- 3. Enter a, b and the height, keeping all three in the same unit.
- 4. Press Calculate to see the area and the arithmetic behind it.
- 5. If your inputs were in feet, the result is square feet; in meters, square meters.
How it works
The formula is area = (a + b) / 2 x height, where a and b are the two parallel sides and height is the perpendicular distance between them. The logic: averaging the two parallel sides and multiplying by the height treats the shape like a rectangle of the same area. That average, (a + b) / 2, is also the midsegment length, the line joining the midpoints of the two non-parallel sides.
Worked examples
Example 1: a = 8, b = 12, height = 5
Add the parallel sides: 8 + 12 = 20. Divide by 2: 20 / 2 = 10, the average side length and the midsegment. Multiply by the height: 10 x 5 = 50. The area is 50 square units.
Example 2: a trapezoid garden bed
A raised bed has parallel edges of 6 ft and 10 ft and is 4 ft across (the perpendicular distance). Add the sides: 6 + 10 = 16. Halve it: 16 / 2 = 8. Multiply by the height: 8 x 4 = 32. The bed covers 32 square feet, the number you need for soil and mulch estimates.
When this tool is useful
- Sizing trapezoid garden beds, patios and plots for soil, gravel or turf.
- Finding the area of a ramp face or tapered concrete form before ordering material.
- Geometry homework where the working matters as much as the area.
- Estimating the cross-section of a ditch, channel or embankment.
What Counts as the Two Parallel Sides
The defining feature is exactly one pair of parallel sides, called the bases, usually of different lengths, which makes the shape taper. The other two sides, the legs, may be equal (an isosceles trapezoid) or different and slant at any angle; none of that changes the area formula.
The height is not a leg, except in a right trapezoid where one leg stands perpendicular. It is the shortest distance between the bases, measured at 90 degrees: on site, measure straight across a bed or form, not along its slanted edge.
Trapezoid or Trapezium?
The naming split confuses international classrooms. American usage: trapezoid = one pair of parallel sides, trapezium = none. British usage reverses them. Whichever word your textbook uses, look at the shape, not the label: with one parallel pair, this formula applies.
Common mistakes to avoid
- Using a slanted side as the height. The height must meet the parallel sides at a right angle; a slanted leg is always longer than the true height.
- Picking the non-parallel sides as a and b. Only the parallel pair goes into the formula.
- Mixing units, such as sides in feet and height in inches, which throws the result off by a factor of 12.
- Dividing by 2 at the wrong step or forgetting it: (a + b) x height without the / 2 doubles the true area.
- Assuming both legs must be equal; they do not, only one parallel pair defines the shape.
Frequently asked questions
What is the formula for the area of a trapezoid?
Area = (a + b) / 2 x height, where a and b are the parallel sides and height is the perpendicular distance between them. Average the parallel sides, then multiply by the height, like a rectangle of that average width.
Which sides are a and b?
The two sides parallel to each other, usually the top and bottom edges in diagrams. The legs, the non-parallel sides, are never used in the area formula; only the height is.
Is a trapezoid the same as a trapezium?
It depends on the country. In US English a trapezoid has one pair of parallel sides and a trapezium has none; British English swaps the meanings. The formula here applies to the one-parallel-pair shape under either name.
How do I find the height if I only measured the slanted side?
With an angle, height = slanted side x sin(angle). With a horizontal offset, use Pythagoras: height = square root of (slant squared minus offset squared). The calculator needs the true perpendicular height.
What is the midsegment shortcut?
The midsegment joins the midpoints of the legs and its length is exactly (a + b) / 2, the average used in the formula. So area also equals midsegment x height, a quick check if you can measure the middle width directly.
Can the formula handle a right trapezoid?
Yes. In a right trapezoid one leg is perpendicular to the parallel sides, so that leg is the height. Enter it as the height and the formula works unchanged.
Bottom line
Average the two parallel sides, multiply by the perpendicular height, and you have the area. Keep the height honest, perpendicular rather than slanted, and the formula works for garden beds, ramps and homework alike.
If the question changes shape, the closest neighbours are Vertex Form Calculator and Sector Area Calculator — or browse everything under Math Calculators.