trapezoid

A trapezoid is a four-sided polygon with at least one pair of parallel sides, called the bases. The other two sides are the legs. In American mathematics, a trapezoid is defined as having at least one pair of parallel sides (parallelograms are included); in some regional conventions the terminology differs and a trapezium may be used for related definitions. The height of a trapezoid is the perpendicular distance between its bases.

Base angles are the angles adjacent to each base. When the bases are parallel, the base angles on a given base are supplementary. An isosceles trapezoid has equal legs, equal base angles, and equal diagonals. A right trapezoid has one leg perpendicular to the bases.

The area of a trapezoid is half the product of the sum of the bases and the height: A = (b1 + b2) × h / 2, where b1 and b2 are the lengths of the bases and h is the height. The perimeter is P = b1 + b2 + l1 + l2, with l1 and l2 the lengths of the legs.

In coordinate or vector form, a trapezoid can be described by its four vertices and can be analyzed using standard polygon formulas, such as the shoelace formula for area. Trapezoids appear in geometry problems, architecture, and design, and their properties—such as isosceles and right variants—provide useful special cases for angle, length, and area calculations.