Trapez

Trapez is a term used in several languages to designate the quadrilateral commonly known in English as a trapezoid or trapezium. Its defining feature is that the figure has a pair of parallel sides, called the bases, while the remaining two sides are the legs. Terminology for this shape varies by region; some traditions use Trapez for a trapezoid with exactly one pair of parallel sides, while others apply the word more broadly to any quadrilateral with a pair of parallel sides.

Etymology and naming conventions reflect its geometric origin. The term traces to Greek trapeza meaning “table,” passed into Latin and then into various European languages. In German, Trapez is the standard name for the trapezoid/trapez; in English, the corresponding terms are trapezium and trapezoid, with usage differing by country.

Geometry and properties. In a trapez, the two parallel sides are called the bases, and the nonparallel sides are the legs. The height is the perpendicular distance between the bases. The area is computed as A = (b1 + b2)/2 × h, where b1 and b2 are the lengths of the bases. Special cases include the isosceles trapezoid, where the legs are equal in length, and the right trapezoid, where a leg is perpendicular to the bases. In an isosceles trapezoid, the diagonals are equal in length.

Additional facts. The segment connecting the midpoints of the legs is parallel to the bases and has a length equal to the average of the base lengths. Opposite angles along a base are supplementary, reflecting the trapez’ linear geometry.

Applications and relevance. Trapezia appear in architecture, design, surveying, and computer graphics as simple yet versatile cross-sectional shapes. They are also used in math education to illustrate area calculations, similarity, and properties of quadrilaterals.