Trapezoid Area
A = ((B+b)·h)/2P = B+b+c+dThe area of a trapezoid is the sum of the two parallel bases, multiplied by the height and divided by two.
Another way to read the same calculation: it is the average of the two bases times the height. A trapezoid behaves like a rectangle whose width is the mean of the longer and shorter base.
The perimeter needs all four measurements, because the non-parallel sides can differ in length.
This is the mistake that dominates trapezoid calculations. The height is the perpendicular distance between the two parallel bases, not the length of the oblique side.
Using the slanted side in place of the height always overestimates the area, and the error grows the more the trapezoid leans.
In the field, the height is measured with a square or a level from the shorter base to the longer one, never along the edge.
- Urban plots with different widths at the front and the back — the most common shape in irregular subdivisions.
- Cross-sections of channels, ditches and dams, where the banks slope.
- Single-pitch roofs with an overhang, and attic walls.
- Joinery pieces and cuts that join two different widths.
Frequently asked questions
The perpendicular distance between the two parallel bases. It is not the slanted side — using that instead always yields an area larger than the real one.
Then it is not a trapezoid. Split the area into triangles and add them up — the standard technique for irregular quadrilaterals.
For the area, no: the formula adds them both before dividing, so the order does not change the result.
For the area, no: the two bases and the height are enough. The non-parallel sides are only needed for the perimeter.