The trapezoid formula
A trapezoid has one pair of parallel sides, called the bases. Its area is the average of the bases times the height:
area = (a + b) ÷ 2 × h
Think of it as a rectangle whose width is the average of the two bases. That average, (a + b) ÷ 2, is also the length of the median, the line through the middle of the trapezoid parallel to the bases.
Worked example
Bases of 6 cm and 10 cm, 4 cm apart: (6 + 10) ÷ 2 × 4 = 8 × 4 = 32 cm².
In the real world
Irregular plots of land, roof slopes, retaining walls, cross-sections of channels and ditches, and gussets in sewing are all trapezoids. For a plot with a 20 m front, 30 m back and 40 m depth: (20 + 30) ÷ 2 × 40 = 1,000 m².
How this works
The page adds the two parallel sides, halves the sum to get the median length, and multiplies by the height (the perpendicular distance between the parallel sides). The lengths of the slanted sides do not affect the area. Results carry your unit, squared for the area. Everything runs in your browser.
Frequently asked
What is the formula for the area of a trapezoid?
(a + b) ÷ 2 × h, with a and b the parallel sides and h the height between them.
Is a trapezoid the same as a trapezium?
In US English trapezoid; in British English trapezium. Both mean one pair of parallel sides here.
Do I need the slanted sides?
Not for the area. You need them for the perimeter.
What is the median of a trapezoid?
The segment joining the midpoints of the legs; its length is the average of the bases.
Sources
Reviewed Oct 17, 2026 · test vectors fixtures/calculators/math/area/trapezoid/