Trapezoid: properties & formulas
A trapezoid (called a trapezium in British English) has a pair of parallel sides. Averaging their lengths and multiplying by the perpendicular distance between them gives its area.
- 4 sides
- 1 pair of parallel sides
- 360° angle sum
- 2 diagonals
Properties of a trapezoid
| Sides / vertices | 4 / 4: two parallel bases and two legs |
|---|---|
| Parallel sides | The bases a and b |
| Height | Perpendicular distance between the bases |
| Angle sum | 360°; the two angles along each leg add to 180° |
| Isosceles trapezoid | Equal legs, equal base angles, and equal diagonals |
| Midsegment | Parallel to the bases, halfway between them |
Trapezoid formulas
| Area | A = (a + b)h / 2 |
|---|---|
| Perimeter | P = a + b + c + d |
| Midsegment | m = (a + b) / 2 |
| Height from area | h = 2A / (a + b) |
| Leg of an isosceles trapezoid | c = √(h² + ((a − b) / 2)²) |
Trapezoid area calculator
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Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
A worked example
For bases 8 and 5 and height 4, the area is (8 + 5) × 4 / 2 = 26 square units.
Trapezoid: common questions
Wondering about the why? Start here.
What are the properties of a trapezoid?
A trapezoid has four sides with at least one pair of parallel sides, called the bases. Its angles add up to 360°, and the two angles along each leg add to 180°. An isosceles trapezoid also has equal legs, equal base angles, and equal diagonals.
Is a trapezoid the same as a trapezium?
In American English, a trapezoid has a pair of parallel sides. In British English that shape is called a trapezium. The area formula A = (a + b)h/2 is the same either way.
Which sides belong in the trapezoid area formula?
Use the two parallel sides a and b, together with their perpendicular separation h: A = (a + b)h/2. The nonparallel sloping sides are not the height. Parallel sides of 8 and 5 with height 4 give area 26 square units.
Explore area formulasCan I find the perimeter from the inputs here?
Not in general. Two parallel side lengths and a height determine area, but they do not uniquely determine the two remaining side lengths. To find perimeter, add all four side lengths when they are known.
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