Trapezoid Area Calculator
The area of a trapezoid (a trapezium in British usage) — average the two parallel sides, then multiply by the height.
A trapezoid has exactly one pair of parallel sides.
How the trapezoid area calculator works
A trapezoid has exactly one pair of parallel sides. Averaging them gives the width of the rectangle that would have the same area, so area = ½(a + b) × h. Put two identical trapezoids together, one flipped, and they form a parallelogram of base (a + b) — which is where the half comes from.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Sides 8 and 5, height 4 | 26 | 26 |
| A shallow embankment | 48 | 48 |
| Equal sides — a rectangle | 30 | 30 |
FAQFrequently asked questions
What is a trapezoid?
A four-sided shape with exactly one pair of parallel sides. British usage calls it a trapezium.
What is the formula?
Half the sum of the parallel sides, times the height: ½(a + b) × h.
Why the half?
Two identical trapezoids fitted together form a parallelogram of base a + b, so one of them is half of that.
Which sides are the parallel ones?
The two that never meet however far you extend them — usually the top and bottom as drawn.
What if both pairs are parallel?
Then it is a parallelogram, and the formula still works because a and b are equal.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.