A trapezoid has two parallel sides of different lengths — its area is the average of those two sides, times the height between them.
How it works
Adding the two parallel base lengths, dividing by 2, and multiplying by the height gives the area.
What this does not include
This does not include an irregular (non-trapezoidal) quadrilateral — this formula specifically requires two sides to be parallel.
How to use this calculator
- Enter both parallel base lengths and the perpendicular height between them.
A worked example
Parallel sides of 8 and 12, height 5: area = (8+12)/2 × 5 = 50.
Parallel sides both 8 (a rectangle), height 5: area = 40 — the standard base × height rectangle formula, since a trapezoid with equal parallel sides is a rectangle or parallelogram.
What the variables mean
| Variable | Meaning |
|---|---|
| Base 1, Base 2 | The two parallel sides |
| Height | Perpendicular distance between the two parallel sides |
Edge cases worth knowing
Equal base lengths collapse the trapezoid into a parallelogram, and the formula still works correctly — it’s a special case, not an error.
A height of zero makes the shape degenerate — flattened to a line with no area — so the calculator declines to show a result. For the reverse problem — solving for a missing base when the area is known — see this site’s trapezoid side calculator.
Frequently asked questions
What counts as the “height” in a trapezoid?
The perpendicular distance between the two parallel sides — not the length of one of the slanted sides, which would overstate the area if used instead.
What happens if both bases are equal length?
The trapezoid becomes a rectangle (or parallelogram), and the formula still works correctly, reducing to simply base times height.
Where is this shape commonly encountered?
Cross-sections of certain roof designs, some countertop or tabletop shapes, and cross-sections of retaining walls or embankments are common real-world trapezoids.
