foursidedness

Foursidedness is the property of having four sides. In geometry, this quality describes polygons with four edges, typically called quadrilaterals or tetragons. The term can also be used more loosely to refer to any figure whose boundary consists of four segments.

In Euclidean plane geometry, a four-sided polygon is closed and non-self-intersecting. The interior angles of any quadrilateral sum to 360 degrees. It has exactly two diagonals, though in concave cases a diagonal may lie outside the shape.

Common examples include the square, rectangle, rhombus, and trapezoid. Irregular quadrilaterals have four sides that are not all equal and may have varied angles. Classification can be by side lengths or by angles. Special families include parallelograms (opposite sides parallel), rectangles (four right angles), rhombi (four equal sides), and squares (four equal sides and four right angles). Some four-sided figures are cyclic (all vertices lie on a common circle) or tangential (a circle can be inscribed).

Applications of foursided figures span mathematics, design, and engineering. They are foundational in tiling, drafting, and computer graphics due to their simplicity and ease of calculating area and perimeter.

Etymology: the term derives from Latin and Greek roots meaning “four” and “angle,” with foursidedness serving as a descriptive noun for the category of four-edged shapes.