tetragon

A tetragon is a polygon with four sides. The name combines Greek tetra- meaning "four" and gōn meaning "angle" or "corner," but in modern mathematics the more common term is quadrilateral.

Tetragons can be classified in several ways. By shape, they may be convex (all interior angles are less than 180 degrees), concave (one interior angle exceeds 180 degrees), or crossed/self-intersecting. By side relations, common families include square, rectangle, rhombus, parallelogram, kite, and trapezoid, though terminology can vary regionally. A square has four equal sides and four right angles; a rectangle has four right angles with opposite sides equal; a rhombus has all sides equal; a kite has two distinct pairs of adjacent equal sides; a trapezoid has at least one pair of parallel sides.

Key properties relate to diagonals and angles. In a parallelogram, the diagonals bisect each other. In a cyclic tetragon, which can be inscribed in a circle, opposite angles sum to 180 degrees. The area of a convex tetragon can be expressed as area = 1/2 d1 d2 sin(theta), where d1 and d2 are the diagonals and theta is the angle between them. Bretschneider's formula provides a general way to compute area from the tetragon’s side lengths and opposite angles.

In usage, the term tetragon is largely historical or analytic, while quadrilateral is the standard term in contemporary geometry, engineering, and surveying. The concept remains a foundational element in polygonal geometry and its applications.

---