Nelikulmaiset

Nelikulmaiset is the Finnish term for quadrilaterals, polygons with four sides and four vertices. In Euclidean geometry they form a broad class that includes common shapes such as rectangles, squares, parallelograms and trapezoids. A nelikulmainen is typically simple, meaning its sides do not cross; convex or concave shapes are both possible. The sum of the interior angles in any nelikulmainen is 360 degrees.

The properties of nelikulmaiset depend on their angles and sides. The diagonals connect opposite vertices and can have varying lengths and angles depending on the shape. In general, area and perimeter are determined by the specific arrangement of sides and angles; for example, in a rectangle the area is length times width, while in a parallelogram it is base times height.

Classification of nelikulmaiset is commonly based on parallelism and angle measures. Parallelograms have two pairs of parallel opposite sides. Rectangles have all angles right. Rhombuses have all sides equal, and squares combine those properties with right angles. Trapezoids (or trapezia) have at least one pair of parallel sides. Quadrilaterals can be convex, with all interior angles less than 180 degrees, or concave, with one interior angle greater than 180 degrees. Some definitions also include self-intersecting forms, but these are not considered simple quadrilaterals in standard geometry.

Nelikulmaiset appear across mathematics and applied fields, including geometry education, architectural design, computer graphics, and surveying. Understanding their properties often relies on angle relationships, parallelism, and symmetry, making them a fundamental topic in planar geometry.