How the trapezoid area formula works
A trapezoid has at least one pair of parallel sides (this page uses the inclusive definition, which counts rectangles and parallelograms as trapezoids). Averaging their lengths gives the width of an equivalent rectangle with the same height, so multiplying that average by the height gives the exact area.
- a — length of the top (one parallel side)
- b — length of the bottom (the other parallel side)
- h — perpendicular height between a and b
More detail
Why the two parallel sides are averaged
A trapezoid can be split into a rectangle and one or two triangles. Averaging the top and bottom lengths — (a + b) / 2 — gives the width of a rectangle with the same area as the trapezoid, so multiplying by the height gives the exact area without needing to know the slanted sides.
Quick check. A trapezoid with top 4, bottom 6, and height 3 gives area (4+6)/2 × 3 = 15 — a fast way to sanity-check the calculator or your own hand math.
Frequently asked questions
What is the area of a trapezoid with top 4, bottom 6, and height 3?
Area = (4 + 6) / 2 × 3 = 5 × 3 = 15. Enter the same numbers above to see the calculator return the identical result.
Which sides count as "top" and "bottom"?
They're the trapezoid's two parallel sides — the ones that never meet. It doesn't matter which one you call "top" (a) versus "bottom" (b); the formula (a + b) / 2 × h gives the same area either way.
Does the height have to be measured straight up and down?
The height must be the perpendicular (shortest) distance between the two parallel sides, not the length of a slanted side. Using a slanted side's length instead of the true height will give an incorrect area.
Why does the calculator show "—"?
That happens when the top, bottom, or height is zero, negative, or blank — a trapezoid needs all three measurements to be positive numbers to have a defined area. It also appears when all three are positive but so large that the product overflows double precision (for example, 1e200 in every field).
Does this formula work for a parallelogram or rectangle too?
Yes. A rectangle and a parallelogram are special cases of a trapezoid where the top and bottom are equal (a = b), so the formula simplifies to Area = a × h, matching the standard rectangle/parallelogram formula.