A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b.

The area of the rectangle is


and its polygon diagonals p and q are of length


A rectangle has a circumcircle with circumradius


but incircle only in the degenerate case of a square.

A number of important topological surfaces can be constructed from the rectangle. Gluing both pairs of opposite edges together with no twists gives a torus, gluing two opposite edges together after giving a half-twist gives a Möbius strip, gluing both pairs of opposite edges together giving one pair a half-twist gives a Klein bottle, and giving both pairs a half-twist gives a projective plane (Stewart 1997).

See also

Blanche's Dissection, Fault-Free Rectangle, Golden Rectangle, Incomparable Rectangles, Klein Bottle, Möbius Strip, Overlapping Rectangles, Perfect Rectangle, Projective Plane, Rectangle Tiling, Rectellipse, Rounded Rectangle, Square, Torus Explore this topic in the MathWorld classroom

Explore with Wolfram|Alpha


Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 122, 1987.Eppstein, D. "Rectilinear Geometry.", H. and Pedoe, D. "Circle and Rectangles." §3.4 in Japanese Temple Geometry Problems. Winnipeg, Manitoba, Canada: Charles Babbage Research Foundation, pp. 43-44 and 125, 1989.Harris, J. W. and Stocker, H. "Rectangle." §3.6.5 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 84, 1998.Kern, W. F. and Bland, J. R. Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. 2, 1948.Stewart, I. "Squaring the Square." Sci. Amer. 277, 94-96, July 1997.

Cite this as:

Weisstein, Eric W. "Rectangle." From MathWorld--A Wolfram Web Resource.

Subject classifications