About the trapezoid area calculator
A trapezoid (called a trapezium in British English) is a four-sided shape with at least one pair of parallel sides. Those two parallel sides are the bases, usually labelled a and b; the other two sides are the legs. This calculator finds the area from the two bases and the perpendicular height, and it also reports the perimeter, the median, and a diagonal estimate from the side lengths you enter.
The area of any trapezoid is the average of its two parallel sides multiplied by the perpendicular distance between them. That single rule covers every trapezoid, whether it is a right trapezoid with one vertical leg, an isosceles trapezoid with two equal legs, or a fully irregular one. The slanted legs change the perimeter and the angles but never the area, so you only need the bases and the height to get the area exactly right.
Trapezoid area comes up constantly in the real world: a gable roof section, a flight of stairs in cross-section, a retaining wall, a garden bed with non-parallel ends, or the cross-section of a canal or channel. Engineers and students also meet it in the trapezoidal rule for estimating the area under a curve.
How the math works
The calculator applies the standard plane-geometry formulas:
Area = (a + b) / 2 x h Median = (a + b) / 2 Perimeter = a + b + c + d
- a and b are the two parallel sides (bases). Their order does not matter since you add them.
- h is the perpendicular height between the bases, measured straight across, not along a slanted leg.
- c and d are the legs (the non-parallel sides); they affect perimeter and angles but not area.
- Median equals the average of the bases, so area can also be read as median times height.
Worked example
Take a trapezoid with a top base of 6 units, a bottom base of 10 units, a height of 5 units, and two legs of 5.4 units each.
- Add the bases: 6 + 10 = 16 units.
- Average them: 16 / 2 = 8 units (this is the median).
- Multiply by height: 8 x 5 = 40 square units. That is the area.
- Perimeter: 6 + 10 + 5.4 + 5.4 = 26.8 units.
- Check: the rectangle on the median (8 x 5 = 40) confirms the area, since the trapezoid and that rectangle share the same average width.
Quick area reference
Area for a height of 5 units across several base pairs, showing how area tracks the average of the two bases.
| Base a | Base b | Average (a+b)/2 | Height | Area |
|---|---|---|---|---|
| 4 | 4 | 4 | 5 | 20 |
| 6 | 10 | 8 | 5 | 40 |
| 8 | 12 | 10 | 5 | 50 |
| 10 | 20 | 15 | 5 | 75 |
| 5 | 25 | 15 | 5 | 75 |
Common pitfalls
- Using a slanted leg as the height. The height must be perpendicular to both bases. Plugging in a leg length inflates the area; drop a vertical line to find the true height.
- Mixing up bases and legs. Only the parallel sides are bases. If you average a base with a leg, the result is meaningless.
- Inconsistent units. Keep every length in the same unit. Mixing feet and inches gives a wrong area; convert first.
- Forgetting area is squared units. If sides are in metres the area is in square metres. Reporting plain units understates the dimension.
- Assuming the legs change the area. They do not. Two trapezoids with the same bases and height have the same area even if one is slanted far more than the other.
Frequently asked questions
What is the formula for the area of a trapezoid?
The area of a trapezoid equals one half times the sum of the two parallel sides times the perpendicular height: A = (a + b) / 2 x h. The parallel sides are usually called the bases, often labelled a and b, and the height is the perpendicular distance between them, not the length of a slanted leg. In words, you average the two parallel sides and multiply by how far apart they are. The slanted legs do not enter the area formula at all.
Why does the trapezoid area formula use the average of the two bases?
A trapezoid can be split into a rectangle plus one or two triangles, and adding their areas simplifies to one half times (a + b) times the height. An easier way to see it: copy the trapezoid, flip the copy, and join it to the original to make a parallelogram whose base is a + b and whose height is h. That parallelogram has area (a + b) x h, and the trapezoid is exactly half of it, so its area is (a + b) / 2 x h, the average of the bases times the height.
What is the median or midline of a trapezoid?
The median, also called the midsegment or midline, is the segment connecting the midpoints of the two non-parallel legs. Its length equals the average of the two parallel sides, (a + b) / 2, which is the same quantity used in the area formula. So the area can also be written as median x height. Because the median is the average of the bases, it always sits exactly halfway between them in length.
Do I need the slanted side lengths to find the area?
No. The area depends only on the two parallel sides and the perpendicular height. The lengths of the slanted legs (c and d) are needed for the perimeter and for angles, but not for the area. A common mistake is to plug a slanted side in where the height belongs; the height must be measured straight across, perpendicular to both parallel sides, otherwise the area comes out too large.
What is an isosceles trapezoid?
An isosceles trapezoid is one whose two non-parallel legs are equal in length, which makes it symmetric about a vertical axis. In that case the base angles are equal and the diagonals are equal too. The area formula is identical, one half times (a + b) times height, because area never depends on the legs. Isosceles trapezoids appear often in roofing, bridges, and furniture design because their symmetry simplifies construction.