quadrilateral

A quadrilateral is a polygon with four sides and four vertices. When the edges do not cross, it is a simple quadrilateral; if the sides cross, it is a crossed quadrilateral. The four sides connect to form a closed figure.

The sum of its interior angles is 360 degrees. The two diagonals join opposite vertices. In a convex quadrilateral, both diagonals lie inside the figure; in a concave one, at least one diagonal lies outside.

Common types include parallelograms (opposite sides parallel), rectangles (parallelograms with right angles), rhombuses (all sides equal), squares (rectangles with equal sides), trapezoids (at least one pair of parallel sides), and kites (two distinct pairs of adjacent equal sides). These classifications can combine, such as a square being both a rectangle and a rhombus.

Area can be found by dividing the figure into two triangles along a diagonal or by applying coordinate methods such as the shoelace formula. In general, area calculations can also use formulas that relate sides and angles, such as Bretschneider’s formula for a general quadrilateral; many practical problems rely on decomposing the figure into simpler shapes.