trapeziaal

Trapeziaal is a four-sided polygon defined by having a pair of parallel sides, known as the bases. In English geometry the same shape is usually called a trapezoid (American usage) or trapezium (British usage). The two other sides are the legs and are not parallel in the common case. The arrangement of the bases and legs gives the trapeziaal its characteristic shape.

Key properties include the bases being parallel and the height, which is the perpendicular distance between the bases. The area is computed as A = (a + b) / 2 × h, where a and b are the lengths of the bases and h is the height. The perimeter is P = a + b + c + d, with c and d being the lengths of the legs. The base angles on the same base are supplementary. Diagonals generally have different lengths, but in an isosceles trapeziaal the diagonals are equal and the base angles are equal as well. A right trapeziaal has one leg perpendicular to the bases.

Notationally, some sources treat trapeziaal as a broader category (at least one pair of parallel sides), while others restrict it to exactly one pair of parallel sides, excluding parallelograms. In many practical contexts the parallelogram is considered distinct, though a parallelogram is sometimes referred to as a special kind of trapeziaal under the inclusive definition.

Applications of trapeziaal shapes appear in design, architecture, cross-sectional analysis, and various engineering problems where a non-parallel side length varies while the bases stay parallel. Etymologically, the term derives from Greek trapezein, meaning to table or to stretch.