Trapézium

A trapezium, also known as a trapezoid in American and Canadian English, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. The angles between a base and the legs are called base angles.

There are different types of trapeziums. A general trapezium has no special properties beyond having one pair of parallel sides. An isosceles trapezium is a trapezium where the non-parallel sides are equal in length. In an isosceles trapezium, the base angles are also equal. A right trapezium is a trapezium that has at least one pair of adjacent angles that are right angles. This implies that one of the legs is perpendicular to both bases.

The area of a trapezium can be calculated using the formula: Area = 0.5 * (sum of bases) * height. The height is the perpendicular distance between the two bases.

The study of trapeziums is a fundamental part of Euclidean geometry. They appear in various geometric constructions and problems. For instance, the concept of a trapezium is used in calculus when approximating the area under a curve using the trapezoidal rule.