Trapezoid Area Calculator
A trapezoid with parallel sides of 8 and 12 and a height of 5 has an area of 50. This trapezoid area calculator uses the classic formula, average the two parallel bases and multiply by the height. It also reports the median, the line through the middle whose length is exactly that base average.
Quick answer
A trapezoid has exactly one pair of parallel sides, called the bases.
Area
50
Median length
10
What this tells you
- •A trapezoid has exactly one pair of parallel sides, called the bases.
- •Its area is the average of the two bases times the perpendicular height.
- •The average works because a trapezoid is a rectangle whose width changes linearly from one base to the other.
- •The height must be the perpendicular distance between the bases, not the slanted side length.
How to Use
- 1Enter the two parallel sides in either order.
- 2Enter the perpendicular height between them.
- 3Read the area, with the median (midsegment) length below.
- 4For a slanted-side measurement, find the true height first with the Pythagorean theorem.
How It Works
Formula
A = (a + b) / 2 x hAveraging the bases finds the width of the equivalent rectangle. For bases 8 and 12, the average is 10, and multiplying by the height of 5 gives an area of 50. Two copies of any trapezoid fit together into a parallelogram with base (a + b) and the same height, which is the one-line proof of the formula.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Bases 8 and 12, height 5
The base average is 10, times the height 5.
A garden bed narrowing from 4 m to 2.5 m over 6 m
Tapered plots are trapezoids, and this is how their soil and turf get estimated.
Roof cross-section, bases 30 and 18, height 9
The trapezoidal gable end of a hip roof, averaged and multiplied.
Trapezoid Areas
Areas for common base pairs and heights.
| Base a | Base b | Height | Area |
|---|---|---|---|
| 4 | 6 | 3 | 15 |
| 8 | 12 | 5 | 50 |
| 10 | 14 | 8 | 96 |
| 5 | 9 | 4 | 28 |
| 20 | 30 | 10 | 250 |
Common mistakes
- Using a slanted leg as the height. The height is the perpendicular gap between the parallel sides, always shorter than the slanted legs.
- Averaging all four sides. Only the two parallel bases enter the formula, the legs contribute nothing to the area.
- Forgetting to halve. Adding the bases without dividing by 2 doubles the area.