firkant

Firkant is the Danish and Norwegian term for a four-sided polygon, commonly translated as quadrilateral in English. The word combines four (fire) and side (kant). It denotes any polygon with four sides and four vertices. In Euclidean geometry, the sum of interior angles of a firkant is 360 degrees. Firkants may be convex, where all interior angles are less than 180 degrees, or concave.

Common subtypes include square, rectangle, rhombus, parallelogram, and trapezoid. A square has four equal sides and four right angles; a rectangle has four right angles; a rhombus has four equal sides; a parallelogram has opposite sides parallel; a trapezoid has at least one pair of parallel sides. All of these are firkants; squares, rectangles, and rhombi are special cases within broader parallelogram families.

Diagonals: In parallelograms, diagonals bisect each other; in rectangles and squares, diagonals are equal in length; in rhombuses, diagonals are perpendicular. These properties assist in geometry problems and in design.

Usage: The term is common in school geometry in Denmark and Norway. In English contexts, quadrilateral is the standard term, while firkant is used when discussing language-specific terminology.