fourangle

Fourangle is a term used to describe a polygon with four sides and four interior angles. In Euclidean geometry, the sum of the interior angles of any fourangle is 360 degrees. The term is not standard in formal mathematics; quadrilateral is the conventional name for this class of figures. A fourangle may be convex, with all interior angles less than 180 degrees, or concave, with one interior angle greater than 180 degrees.

Classification of fourangles can be based on side lengths and angle relations. A square has four equal sides and four right angles. A rectangle has four right angles but opposite sides are equal and parallel. A rhombus has four equal sides but angles are not necessarily right. A kite has two distinct pairs of adjacent equal sides. A parallelogram has opposite sides parallel, which encompasses rectangles and rhombuses as special cases. A trapezoid (US usage; trapezium in some regions) has at least one pair of opposite sides parallel. A cyclic fourangle is one whose vertices lie on a common circle; such figures have additional area properties.

Area calculation for a general fourangle depends on sides and angles; there is no single formula applicable to all fourangles. Common methods include dividing the figure into two triangles, applying base-height formulas, or using coordinate geometry. For cyclic fourangles, Brahmagupta’s formula provides the area in terms of the side lengths.

Usage notes: fourangle is a descriptive, literal term that may appear in informal contexts. Quadrilateral remains the standard term in mathematics and geometry curricula. See also quadrilateral, polygon, Euclidean geometry.