trapezformade

Trapezformade is a quadrilateral defined by having exactly one pair of parallel sides, known as the bases; the remaining two sides, the legs, are not parallel. This makes it the planar analogue of a trapezoid in many geometric traditions. The distance between the bases is the height h, and with base lengths b1 and b2 the area is A = (b1 + b2) × h / 2.

Angles and diagonals: The sum of interior angles of any quadrilateral is 360 degrees. Because the bases are parallel, consecutive angles along each leg are supplementary. In an isosceles trapezformade, where the legs are equal, the diagonals are equal in length; in a general trapezformade the diagonals are typically of different lengths and intersect inside the figure.

Variants: A right trapezformade has one leg perpendicular to the bases; an isosceles trapezformade has equal legs and equal diagonals. A cyclic trapezformade may occur when opposite angles sum to 180 degrees.

Construction and relations: To construct one, place two parallel lines and choose two points on one line, then connect each to a point on the other line so that the resulting quadrilateral has exactly one parallel pair of opposite sides. Trapezformades are related to other quadrilaterals such as parallelograms, rectangles, and general trapezoids, sharing area formulas and angle properties.