Trapezoide

Trapezoide, known in English as trapezoid (trapezium in some varieties), is a quadrilateral defined by having a single pair of parallel sides. The parallel sides are called bases, while the non-parallel sides are called legs. The distance between the bases is the height.

The area of a trapezoide is given by the formula A = (b1 + b2) / 2 × h, where b1 and b2 are the lengths of the bases and h is the height. The bases are parallel, and the height is measured perpendicular to them. The sum of the interior angles on each leg is 180 degrees.

In a trapezoide, the base angles adjacent to each base are supplementary. When the legs are equal in length, the trapezoide is called isosceles, and its diagonals are equal in length. A right trapezoide has two right angles, typically with one leg perpendicular to the bases. The diagonals of a trapezoide generally have different lengths, except in special symmetric cases.

Some definitions treat trapezoide as any quadrilateral with at least one pair of parallel sides, in which case parallelograms and rectangles may be included. In stricter definitions, a trapezoide has exactly one pair of parallel sides, excluding parallelograms.

Applications of trapezoide occur in architecture, design, and surveying, where its properties help model ramps, roof structures, and cross-sections. It also appears in various geometric problems and theorems, illustrating relationships between bases, legs, heights, and diagonals.