Area of a Trapezoid Calculator — ½ × (a + b) × h
Enter the two parallel sides and the height of a trapezoid to get its area, midline and perimeter. Optionally enter the leg length for a non-isosceles trapezoid; otherwise the calculator assumes an isosceles trapezoid and computes the legs automatically.
Area = ½ × (a + b) × h
- 1
Sum of parallel sides
8 + 4 = 12 - 2
Average (midline)
(8 + 4) ÷ 2 = 6The midline equals the average of the two bases — this is the effective width. - 3
Area
6 × 5 = 30
How does this calculator work?
Area of a trapezoid = ½ × (a + b) × h, where a and b are the two parallel sides and h is the perpendicular height between them. The midline = (a + b)/2. For the perimeter, add the two legs; if isosceles, each leg = √(h² + ((a−b)/2)²).
Formula
How this is calculated
A trapezoid (called a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides, called the bases (a and b). The height h is the perpendicular distance between the bases — not the length of the slant sides (legs). The area formula Area = ½ × (a + b) × h comes from treating the trapezoid as the average of two rectangles: one with width a and one with width b, each of height h.
The midline (also called the midsegment or median) of a trapezoid connects the midpoints of the two legs. Its length equals the average of the two bases: Midline = (a + b) / 2. The area can also be written as Area = Midline × h, which is handy to remember.
For the perimeter you also need the two leg (non-parallel side) lengths. If the trapezoid is isosceles (the legs are equal), each leg has length √(h² + ((a − b)/2)²), derived from the right triangle formed by the height and the horizontal offset of the top base relative to the bottom. If you have a non-isosceles trapezoid, enter the leg length directly and the calculator uses it for both legs (add both legs manually if they differ).
Frequently asked questions
In US English, a trapezoid has exactly one pair of parallel sides. In British English the same shape is called a trapezium. The formulas are identical — the naming is purely regional.
If you know the leg length c and the base lengths a and b, the height of an isosceles trapezoid is h = √(c² − ((a−b)/2)²). For a non-isosceles trapezoid with both legs, use the same formula for each leg and its horizontal projection, then compute h from that.
Yes — a parallelogram is a special trapezoid where both pairs of sides are parallel, i.e. a = b. Setting a = b gives Area = a × h, the standard parallelogram formula. A rectangle is a parallelogram with h = leg.
Also known as
TG we-Calculate Editorial Team. (2026). Area of a Trapezoid Calculator — ½ × (a + b) × h [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/area-of-a-trapezoid-calculator
TG we-Calculate Editorial Team. "Area of a Trapezoid Calculator — ½ × (a + b) × h." TG we-Calculate. 2026. https://we-calculate.com/calculator/area-of-a-trapezoid-calculator.
TG we-Calculate Editorial Team, "Area of a Trapezoid Calculator — ½ × (a + b) × h," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/area-of-a-trapezoid-calculator
@misc{wecalculate_area_of_a_trapezoid_calculator, title = {Area of a Trapezoid Calculator — ½ × (a + b) × h}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/area-of-a-trapezoid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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