Vierkanten

Vierkanten are polygons with four sides and four vertices. In geometry they are typically called quadrilaterals. The sum of the interior angles in any vierkant is 360 degrees. Vierkanten can be convex (all angles less than 180 degrees) or concave (one angle greater than 180 degrees). They are usually simple, meaning they do not cross themselves, although there are also crossed quadrilaterals in broader definitions.

Common classifications include:

- Parallelogram: opposite sides are parallel.

- Rectangle: a parallelogram with four right angles.

- Rhombus: all four sides have equal length.

- Square: a rectangle with four equal sides (both a rectangle and a rhombus).

- Trapezium (trapezoid in American terminology): at least one pair of opposite sides is parallel.

- Kite: two distinct pairs of adjacent sides are equal.

Diagonals are often used to distinguish and analyze vierkanten. In a rectangle, diagonals are equal in length. In a rhombus, diagonals are perpendicular. In a square, diagonals are both equal and perpendicular. In a general parallelogram, diagonals bisect each other.

Area can be found in several ways. For a rectangle, area equals length times width. For a general vierkant, area can be computed by dividing the shape into triangles or, more generally, by using the formula area = 1/2 d1 d2 sin(theta), where d1 and d2 are the lengths of the diagonals and theta is the angle between them.

Vierkanten are fundamental in geometry, tiling, architecture, computer graphics, and many practical design applications. See also quadrilateral and polygon for related concepts.