trapesium

Trapesium is a four‑sided polygon characterized by having one pair of parallel sides, which are called the bases. The other two sides are non‑parallel and are referred to as the legs. The distance between the bases is the height of the figure. In many curricula, a trapezium (or trapezoid, depending on regional terminology) is the shape formed by these properties.

The area of a trapezium is computed by the formula A = (b1 + b2) / 2 × h, where b1 and b2 are the lengths of the two bases and h is the height (the perpendicular distance between the bases). The perimeter is P = b1 + b2 + a + c, with a and c representing the lengths of the legs. A segment connecting the midpoints of the legs is parallel to the bases and has length equal to the average of the bases: (b1 + b2) / 2. This midsegment is often useful in geometric problems.

There are several common types of trapeziums. An isosceles trapezium has equal legs, and in such figures the diagonals are equal in length. A right trapezium has at least one leg perpendicular to the bases. Depending on regional terminology, some sources distinguish trapezium from trapezoid by different criteria, and the terms may be used interchangeably in various educational contexts.

Applications of trapeziums appear in architecture, design, and everyday measurements, where the ability to compute area, height, or segment lengths using base lengths is useful.