A trapezoid (called a trapezium in British English) is a four-sided flat shape with exactly one pair of parallel sides. Those two parallel sides are its bases, and the perpendicular distance between them is the height. This calculator applies the exact area formula to find any one of those three quantities when you know the other two — no memorising, no rearranging by hand.
The formula
The area of a trapezoid is:
A = (a + b) / 2 × h
where a is the top (shorter) base, b is the bottom (longer) base, and h is
the perpendicular height. The factor (a + b) / 2 is the midsegment — the average
width — and multiplying that average width by the height gives the enclosed area, just as
for a rectangle.
Rearranging for the other unknowns:
- Height:
h = 2A / (a + b) - Top base:
a = 2A / h − b - Bottom base:
b = 2A / h − a
All four versions are built into the Solve-for dropdown above.
How it works
- Select what you want to find from the Solve for menu.
- Fill in the known values — the inputs for the quantity you are solving for are hidden automatically.
- The result, the formula used, and the full step-by-step working appear immediately below.
- An SVG diagram updates to show the relative proportions of the trapezoid you entered.
- Click Copy result to grab the answer, formula, and working in one go.
Everything runs entirely in your browser. No data is sent to a server.
Worked example
A cross-section of a drainage channel is trapezoidal. The bottom (narrower) base is 6 m, the top (wider) base is 10 m, and the perpendicular depth is 4 m.
Step 1 — average the bases: (6 + 10) / 2 = 8 m
Step 2 — multiply by height: 8 × 4 = 32 m²
So the cross-sectional area is 32 square metres. If the engineer later discovers the cross-section must carry 40 m² of flow and asks “how deep does the channel need to be?”:
h = 2 × 40 / (6 + 10) = 80 / 16 = 5 m
Both calculations take one click in this tool.
| Top base (a) | Bottom base (b) | Height (h) | Area |
|---|---|---|---|
| 5 | 9 | 4 | 28 |
| 8 | 12 | 5 | 50 |
| 3 | 7 | 6 | 30 |
| 10 | 10 | 8 | 80 (rectangle) |
Note the last row: when both bases are equal the trapezoid becomes a rectangle and the formula reduces to A = b × h, confirming the result.
Why the formula works
Imagine placing a copy of the trapezoid upside-down alongside the original. The two
together form a parallelogram whose base is (a + b) and whose height is h, so its
area is (a + b) × h. The original trapezoid is exactly half that parallelogram, giving
A = (a + b) / 2 × h. Alternatively, you can split the trapezoid into a rectangle and
two right triangles and add their areas — the result is the same formula.