The area formula
A = (B + b) ÷ 2 × h
Where the formula comes from
Take a trapezoid, copy it, rotate the copy 180° and join the two: you get a parallelogram with base B + b and height h. Its area is (B + b)h, so the trapezoid is half that. The same reasoning explains why the median equals (B + b)/2 — it is the width at the height where the shape averages out.
A worked example, step by step
A trapezoid with bases of 10 cm and 6 cm and a height of 4 cm
- Sum of the bases: 10 + 6 = 16 cm.
- Average: 16 ÷ 2 = 8 cm.
- Area: 8 × 4 = 32 cm².
- The median is also 8 cm.
Watch the units: area is always in square units.
Where it turns up in practice
Land measurement, where irregular plots are broken into trapezoids; road and canal cross-sections, which are trapezoidal almost by definition; and the trapezoidal rule in numerical integration, which approximates any curve with a strip of trapezoids.