Trapezoid

A trapezoid (called trapezium in British English — names reversed from US usage!) is a quadrilateral with at least one pair of parallel sides, called the bases. The non-parallel sides are the legs.

Area: $A = \frac{1}{2}(b_1 + b_2) h$, where $b_1, b_2$ are the parallel sides and $h$ is the perpendicular distance between them. Intuition: average the two bases, treat as a rectangle of that average width.

Special types:

• Isosceles trapezoid: legs equal length; base angles equal.
• Right trapezoid: one leg perpendicular to the bases.

Trapezoidal area is the basis of the trapezoidal rule in numerical integration: approximate the area under a curve by a series of trapezoids — more accurate than rectangles (Riemann sum) but simpler than Simpson's rule.