Trapezoid Area Calculator

The formula

A trapezoid (called a trapezium in British English) has two parallel sides, a and b. Its area is the average of those two sides times the height:

Area = (a + b) ÷ 2 × h

The height h is the perpendicular distance between the two parallel sides — not the length of a slanted side.

Worked examples

• Parallel sides of 6 m and 10 m, 4 m apart: (6 + 10) ÷ 2 × 4 = 32 m².
• A plot of land with a 20 m frontage, a 30 m back boundary and 40 m between them: (20 + 30) ÷ 2 × 40 = 1,000 m².
• The wall under a sloping roof, 2 m high on one side and 3.2 m on the other, 5 m wide: (2 + 3.2) ÷ 2 × 5 = 13 m² to paint.

Why the formula works

Put two identical trapezoids together, one upside down, and they form a parallelogram with base (a + b) and the same height. Its area is (a + b) × h, so one trapezoid is half of that. The formula also covers special cases: if a = b, the shape is a rectangle (a × h); if one side shrinks to zero, it becomes a triangle (b × h ÷ 2).

Finding the height

If you know the slanted side but not the height, use Pythagoras in the right triangle formed at the end. For an isosceles trapezoid with parallel sides 6 and 10 and slanted sides of 5:

• The overhang on each side is (10 − 6) ÷ 2 = 2
• Height = √(5² − 2²) = √21 ≈ 4.58
• Area = 8 × 4.58 ≈ 36.7

Practical uses

Trapezoids are everywhere in building and land measurement: roof sections, embankment cross-sections, retaining walls, irregular plots. For more complex shapes, split them into rectangles, triangles and trapezoids and add the areas. The area converter turns the result into hectares, acres or square feet.

Formulas and content last reviewed: October 2026 · About