Trapetsio

Trapetsio is a term used in several languages to denote the geometric figure commonly known in English as a trapezoid or trapezium. It refers to a simple quadrilateral that has at least one pair of parallel sides, called the bases. The other two sides are non-parallel and are called the legs.

In standard Euclidean geometry, the distance between the bases is called the height. The area of a trapetsio is given by A = (b1 + b2) × h / 2, where b1 and b2 are the lengths of the two bases and h is the height. The line segment joining the midpoints of the legs (the mid-segment) is parallel to the bases and has length (b1 + b2) / 2.

Diagonals of a trapetsio are not generally equal; they are equal only in the isosceles case, where the legs are congruent. The sum of interior angles in any trapetsio is 360 degrees. A right trapetsio has a leg perpendicular to the bases, creating two right angles at the base intersection.

Variations include the isosceles trapetsio and the right trapetsio; the term trapetsio may be used interchangeably with trapezium or trapezoid depending on regional definitions, and some conventions distinguish trapezoid as having exactly one pair of parallel sides from trapezium, which may have more than one parallel pair in some languages.

Etymology: the term derives from Greek roots related to “table,” reflecting an early association with a tabletop shape.