Quadrangulares

Quadrangulares is a term used in some languages to denote polygons with four sides and four interior angles; in English the standard term is quadrilateral. The category includes both simple, non-self-intersecting four-sided figures and, in some contexts, crossed quadrilaterals where the sides cross each other. These shapes are ubiquitous in geometry and appear in many real-world contexts.

Quadrangulares are classified in multiple ways. By parallelism: parallelograms (including rectangles, squares, and rhombi) have opposite sides parallel; trapezoids have exactly one pair of parallel sides. By angle measures: rectangles have four right angles; squares have equal sides and right angles; rhombuses have equal sides; cyclic quadrilaterals can be inscribed in a circle with opposite angles summing to 180 degrees.

Key properties include that for any simple quadrilateral the interior angle sum is 360 degrees. The area of a convex quadrilateral can be computed as one-half the product of its diagonals times the sine of the angle between them: Area = 1/2 d1 d2 sin(phi). The diagonals also reveal many other relations, and formulas such as Bretschneider’s give area from side lengths and opposite angles in general cases.

Applications of quadrangulares range from mathematics education to engineering and computer graphics, design and surveying, where four-sided shapes serve as building blocks for more complex structures.