rect

Rect is short for rectangle, a four-sided polygon with four right angles. In Euclidean geometry, a rectangle is a parallelogram with all angles equal to 90 degrees; equivalently, a parallelogram with consecutive sides perpendicular. Opposite sides are parallel and equal in length.

Key properties include: diagonals that are equal in length and bisect each other; opposite sides that are parallel and equal; and symmetry features such as two lines of symmetry (through the midpoints of opposite sides) and rotational symmetry of 180 degrees.

Formulas often used with rectangles: area equals length times width (A = l × w); perimeter equals twice the sum of length and width (P = 2(l + w)); and the length of a diagonal equals the square root of the sum of the squares of the sides (d = √(l² + w²)). In coordinate geometry, an axis-aligned rectangle can be defined by its corners (x1, y1), (x2, y2) with x1 < x2 and y1 < y2, yielding vertices at (x1, y1), (x2, y1), (x2, y2), (x1, y2).

In computing and software, rect or Rect commonly denotes a rectangular region in a coordinate space, often represented by properties such as x, y, width, height or by left, top, right, bottom. Rect data structures are foundational in graphical user interfaces, image processing, and spatial queries, serving as bounding boxes, clipping regions, or layout units.

Related shapes include the square (a rectangle with all sides equal) and the general parallelogram. Rectangles are ubiquitous in design, architecture, mathematics, and computer science due to their simplicity and predictable properties.