# Rectangle

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Quadrilateral with four right angles

For the record label, see [Rectangle (label)](/source/Rectangle_(label)).

Rectangle Rectangle Type quadrilateral, trapezium, parallelogram, orthotope Edges and vertices 4 Schläfli symbol { } × { } Coxeter–Dynkin diagrams Symmetry group Dihedral (D2), [2], (*22), order 4 Properties convex, isogonal, cyclic Opposite angles and sides are congruent Dual polygon rhombus

In [Euclidean plane geometry](/source/Euclidean_geometry), a **rectangle** is a [rectilinear](/source/Rectilinear_polygon) [convex polygon](/source/Convex_polygon) or a [quadrilateral](/source/Quadrilateral) with four [right angles](/source/Right_angle). It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a [parallelogram](/source/Parallelogram) containing a right angle. A rectangle with four sides of equal length is a *[square](/source/Square)*. The term "[oblong](https://en.wiktionary.org/wiki/oblong)" is used to refer to a non-[square](/source/Square) rectangle.[1][2][3] A rectangle with [vertices](/source/Vertex_(geometry)) *ABCD* would be denoted as *ABCD*.

The word rectangle comes from the [Latin](/source/Latin) *rectangulus*, which is a combination of *rectus* (as an adjective, right, proper) and *angulus* ([angle](/source/Angle)).

A **[crossed rectangle](#Crossed_rectangles)** is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals[4] (therefore only two sides are parallel). It is a special case of an [antiparallelogram](/source/Antiparallelogram), and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as [spherical](/source/Spherical_geometry), [elliptic](/source/Elliptic_geometry), and [hyperbolic](/source/Hyperbolic_geometry), have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.

Rectangles are involved in many [tiling](#Tessellations) problems, such as tiling the plane by rectangles or tiling a rectangle by [polygons](/source/Polygon).

## Characterizations

A [convex](/source/Convex_polygon) [quadrilateral](/source/Quadrilateral) is a rectangle [if and only if](/source/If_and_only_if) it is any one of the following:[5][6]

- a [parallelogram](/source/Parallelogram) with at least one [right angle](/source/Right_angle)

- a parallelogram with [diagonals](/source/Diagonal) of equal length

- a parallelogram *ABCD* where [triangles](/source/Triangle) *ABD* and *DCA* are [congruent](/source/Congruence_(geometry))

- an equiangular quadrilateral

- a quadrilateral with four right angles

- a quadrilateral where the two diagonals are equal in length and [bisect](/source/Bisection) each other[7]

- a convex quadrilateral with successive sides *a*, *b*, *c*, *d* whose area is 1 4 ( a + c ) ( b + d ) {\displaystyle {\tfrac {1}{4}}(a+c)(b+d)} .[8]: fn.1

- a convex quadrilateral with successive sides *a*, *b*, *c*, *d* whose area is 1 2 ( a 2 + c 2 ) ( b 2 + d 2 ) . {\displaystyle {\tfrac {1}{2}}{\sqrt {(a^{2}+c^{2})(b^{2}+d^{2})}}.} [8]

## Classification

A rectangle is a special case of both [parallelogram](/source/Parallelogram) and [trapezoid](/source/Trapezoid). A [square](/source/Square) is a special case of a rectangle.

### Traditional hierarchy

A rectangle is a special case of a [parallelogram](/source/Parallelogram) in which each pair of adjacent [sides](/source/Edge_(geometry)) is [perpendicular](/source/Perpendicular).

A parallelogram is a special case of a trapezium (known as a [trapezoid](/source/Trapezoid) in North America) in which *both* pairs of opposite sides are [parallel](/source/Parallel_(geometry)) and [equal](/source/Equality_(mathematics)) in [length](/source/Length).

A trapezium is a [convex](/source/Convex_polygon) [quadrilateral](/source/Quadrilateral) which has at least one pair of [parallel](/source/Parallel_(geometry)) opposite sides.

A convex quadrilateral is

- **[Simple](/source/Simple_polygon)**: The boundary does not cross itself.

- **[Star-shaped](/source/Star-shaped_polygon)**: The whole interior is visible from a single point, without crossing any edge.

### Alternative hierarchy

De Villiers defines a rectangle more generally as any quadrilateral with [axes of symmetry](/source/Reflection_symmetry) through each pair of opposite sides.[9] This definition includes both right-angled rectangles and crossed rectangles. Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another which is the [perpendicular](/source/Perpendicular) bisector of those sides, but, in the case of the crossed rectangle, the first [axis](/source/Axis_of_symmetry) is not an axis of [symmetry](/source/Symmetry) for either side that it bisects.

Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides. These quadrilaterals comprise [isosceles trapezia](/source/Isosceles_trapezia) and crossed isosceles trapezia (crossed quadrilaterals with the same [vertex arrangement](/source/Vertex_arrangement) as isosceles trapezia).

## Properties

### Symmetry

A rectangle is [cyclic](/source/Cyclic_polygon): all [corners](/source/Corner_angle) lie on a single [circle](/source/Circle).

It is [equiangular](/source/Equiangular_polygon): all its corner [angles](/source/Angle) are equal (each of 90 [degrees](/source/Degree_(angle))).

It is isogonal or [vertex-transitive](/source/Vertex-transitive): all corners lie within the same [symmetry orbit](/source/Symmetry_orbit).

It has two [lines](/source/Line_(geometry)) of [reflectional symmetry](/source/Reflectional_symmetry) and [rotational symmetry](/source/Rotational_symmetry) of order 2 (through 180°).

### Rectangle-rhombus duality

The [dual polygon](/source/Dual_polygon) of a rectangle is a [rhombus](/source/Rhombus), as shown in the table below.[10]

Rectangle Rhombus All angles are equal. All sides are equal. Alternate sides are equal. Alternate angles are equal. Its centre is equidistant from its vertices, hence it has a circumcircle. Its centre is equidistant from its sides, hence it has an incircle. Two axes of symmetry bisect opposite sides. Two axes of symmetry bisect opposite angles. Diagonals are equal in length. Diagonals intersect at equal angles. All angles are right angles; opposite sides are equal and parallel All sides are equal; opposite sides are parallel.

- The figure formed by joining, in order, the midpoints of the sides of a rectangle is a [rhombus](/source/Rhombus) and vice versa.

### Miscellaneous

A rectangle is a [rectilinear polygon](/source/Rectilinear_polygon): its sides meet at right angles.

A rectangle in the plane can be defined by five independent [degrees of freedom](/source/Degrees_of_freedom_(mechanics)) consisting, for example, of three for position (comprising two of [translation](/source/Translation_(geometry)) and one of [rotation](/source/Rotation)), one for shape ([aspect ratio](/source/Aspect_ratio#Rectangles)), and one for overall size (area).

Two rectangles, neither of which will fit inside the other, are said to be [incomparable](/source/Comparability).

## Formulae

The formula for the perimeter of a rectangle

The area of a rectangle is the product of the length and width.

If a rectangle has length ℓ {\displaystyle \ell } and width w {\displaystyle w} , then:[11]

- it has [area](/source/Area) A = ℓ w {\displaystyle A=\ell w\,} ;

- it has [perimeter](/source/Perimeter) P = 2 ℓ + 2 w = 2 ( ℓ + w ) {\displaystyle P=2\ell +2w=2(\ell +w)\,} ;

- each diagonal has length d = ℓ 2 + w 2 {\displaystyle d={\sqrt {\ell ^{2}+w^{2}}}} ; and

- when ℓ = w {\displaystyle \ell =w\,} , the rectangle is a [square](/source/Square_(geometry)).[1]

## Theorems

The [isoperimetric theorem](/source/Isoperimetric_theorem) for rectangles states that among all rectangles of a given [perimeter](/source/Perimeter), the square has the largest [area](/source/Area).

The midpoints of the sides of any [quadrilateral](/source/Quadrilateral) with [perpendicular](/source/Perpendicular) [diagonals](/source/Diagonals) form a rectangle.

A [parallelogram](/source/Parallelogram) with equal [diagonals](/source/Diagonals) is a rectangle.

The [Japanese theorem for cyclic quadrilaterals](/source/Japanese_theorem_for_cyclic_quadrilaterals)[12] states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a time form a rectangle.

The [British flag theorem](/source/British_flag_theorem) states that with vertices denoted *A*, *B*, *C*, and *D*, for any point *P* on the same plane of a rectangle:[13]

- ( A P ) 2 + ( C P ) 2 = ( B P ) 2 + ( D P ) 2 . {\displaystyle \displaystyle (AP)^{2}+(CP)^{2}=(BP)^{2}+(DP)^{2}.}

For every convex body *C* in the plane, we can [inscribe](/source/Inscribed_figure) a rectangle *r* in *C* such that a [homothetic](/source/Homothetic_transformation) copy *R* of *r* is circumscribed about *C* and the positive homothety ratio is at most 2 and 0.5 × Area ( R ) ≤ Area ( C ) ≤ 2 × Area ( r ) {\displaystyle 0.5{\text{ × Area}}(R)\leq {\text{Area}}(C)\leq 2{\text{ × Area}}(r)} .[14]

There exists a unique rectangle with sides a {\displaystyle a} and b {\displaystyle b} , where a {\displaystyle a} is less than b {\displaystyle b} , with two ways of being folded along a line through its center such that the area of overlap is minimized and each area yields a different shape – a triangle and a pentagon. The unique ratio of side lengths is a b = 0.815023701... {\displaystyle \displaystyle {\frac {a}{b}}=0.815023701...} .[15]

## Crossed rectangles

A [*crossed*](/source/List_of_self-intersecting_polygons) *quadrilateral* (self-intersecting) consists of two opposite sides of a non-self-intersecting quadrilateral along with the two diagonals. Similarly, a crossed rectangle is a *crossed quadrilateral* which consists of two opposite sides of a rectangle along with the two diagonals. It has the same [vertex arrangement](/source/Vertex_arrangement) as the rectangle. It appears as two identical triangles with a common vertex, but the geometric intersection is not considered a vertex.

A *crossed quadrilateral* is sometimes likened to a [bow tie](/source/Bow_tie) or [butterfly](/source/Butterfly), sometimes called an "angular eight". A [three-dimensional](/source/Three-dimensional) rectangular [wire](/source/Wire) [frame](/source/Space_frame) that is twisted can take the shape of a bow tie.

The interior of a *crossed rectangle* can have a [polygon density](/source/Polygon_density) of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise.

A *crossed rectangle* may be considered [equiangular](/source/Equiangular_polygon) if right and left turns are allowed. As with any *crossed quadrilateral*, the sum of its [interior angles](/source/Interior_angle) is 720°, allowing for internal angles to appear on the outside and exceed 180°.[16]

A rectangle and a crossed rectangle are quadrilaterals with the following properties in common:

- Opposite sides are equal in length.

- The two diagonals are equal in length.

- It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).

## Other rectangles

A **saddle rectangle** has 4 nonplanar vertices, [alternated](/source/Alternation_(geometry)) from vertices of a [rectangular cuboid](/source/Rectangular_cuboid), with a unique [minimal surface](/source/Minimal_surface) interior defined as a linear combination of the four vertices, creating a saddle surface. This example shows 4 blue edges of the rectangle, and two [green](/source/Green) diagonals, all being diagonal of the cuboid rectangular faces.

In [spherical geometry](/source/Spherical_geometry), a **spherical rectangle** is a figure whose four edges are [great circle](/source/Great_circle) arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. The surface of a sphere in Euclidean solid geometry is a non-Euclidean surface in the sense of elliptic geometry. Spherical geometry is the simplest form of elliptic geometry.

In [elliptic geometry](/source/Elliptic_geometry), an **elliptic rectangle** is a figure in the elliptic plane whose four edges are elliptic arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length.

In [hyperbolic geometry](/source/Hyperbolic_geometry), a **hyperbolic rectangle** is a figure in the hyperbolic plane whose four edges are hyperbolic arcs which meet at equal angles less than 90°. Opposite arcs are equal in length.

## Tessellations

The rectangle is used in many periodic [tessellation](/source/Tessellation) patterns, in [brickwork](/source/Brickwork), for example, these tilings:

Stacked bond Running bond Basket weave Basket weave Herringbone pattern

## Squared, perfect, and other tiled rectangles

A perfect rectangle of order 9

Lowest-order perfect squared square (1) and the three smallest perfect squared squares (2–4) – all are simple squared squares

A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangulated" (or "triangled") rectangle respectively. The tiled rectangle is *perfect*[17][18] if the tiles are [similar](/source/Similarity_(geometry)) and finite in number and no two tiles are the same size. If two such tiles are the same size, the tiling is *imperfect*. In a perfect (or imperfect) triangled rectangle the triangles must be [right triangles](/source/Right_triangle). A database of all known perfect rectangles, perfect squares and related shapes can be found at [squaring.net](http://www.squaring.net/). The lowest number of squares need for a perfect tiling of a rectangle is 9[19] and the lowest number needed for a [perfect tilling a square](/source/Squaring_the_square) is 21, found in 1978 by computer search.[20]

A rectangle has [commensurable](/source/Commensurability_(mathematics)) sides if and only if it is tileable by a finite number of unequal squares.[17][21] The same is true if the tiles are unequal isosceles [right triangles](https://en.wiktionary.org/wiki/right_triangle).

The tilings of rectangles by other tiles which have attracted the most attention are those by congruent non-rectangular [polyominoes](/source/Polyomino), allowing all rotations and reflections. There are also tilings by congruent [polyaboloes](/source/Polyabolo).

## Unicode

The following [Unicode](/source/Unicode) code points depict rectangles:

   U+25AC ▬ BLACK RECTANGLE
   U+25AD ▭ WHITE RECTANGLE
   U+25AE ▮ BLACK VERTICAL RECTANGLE
   U+25AF ▯ WHITE VERTICAL RECTANGLE

## See also

- [Cuboid](/source/Cuboid)

- [Golden rectangle](/source/Golden_rectangle)

- [Hyperrectangle](/source/Hyperrectangle)

- [Superellipse](/source/Superellipse) (includes a rectangle with rounded corners)

## References

1. ^ [***a***](#cite_ref-:0_1-0) [***b***](#cite_ref-:0_1-1) Tapson, Frank (July 1999). ["A Miscellany of Extracts from a Dictionary of Mathematics"](https://web.archive.org/web/20140514200449/http://www.cimt.plymouth.ac.uk/resources/topics/art002.pdf) (PDF). Oxford University Press. Archived from [the original](http://www.cimt.plymouth.ac.uk/resources/topics/art002.pdf) (PDF) on 2014-05-14. Retrieved 2013-06-20.

1. **[^](#cite_ref-2)** ["Definition of Oblong"](https://www.mathsisfun.com/definitions/oblong.html). *Math Is Fun*. Retrieved 2011-11-13.

1. **[^](#cite_ref-3)** [Oblong – Geometry – Math Dictionary](http://www.icoachmath.com/SiteMap/Oblong.html) [Archived](https://web.archive.org/web/20090408184018/http://www.icoachmath.com/SiteMap/Oblong.html) 2009-04-08 at the [Wayback Machine](/source/Wayback_Machine). Icoachmath.com. Retrieved 2011-11-13.

1. **[^](#cite_ref-4)** [Coxeter, Harold Scott MacDonald](/source/Harold_Scott_MacDonald_Coxeter); Longuet-Higgins, M.S.; Miller, J.C.P. (1954). "Uniform polyhedra". *Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences*. **246** (916). The Royal Society: 401–450. [Bibcode](/source/Bibcode_(identifier)):[1954RSPTA.246..401C](https://ui.adsabs.harvard.edu/abs/1954RSPTA.246..401C). [doi](/source/Doi_(identifier)):[10.1098/rsta.1954.0003](https://doi.org/10.1098%2Frsta.1954.0003). [ISSN](/source/ISSN_(identifier)) [0080-4614](https://search.worldcat.org/issn/0080-4614). [JSTOR](/source/JSTOR_(identifier)) [91532](https://www.jstor.org/stable/91532). [MR](/source/MR_(identifier)) [0062446](https://mathscinet.ams.org/mathscinet-getitem?mr=0062446). [S2CID](/source/S2CID_(identifier)) [202575183](https://api.semanticscholar.org/CorpusID:202575183).

1. **[^](#cite_ref-5)** Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, pp. 34–36 [ISBN](/source/ISBN_(identifier)) [1-59311-695-0](https://en.wikipedia.org/wiki/Special:BookSources/1-59311-695-0).

1. **[^](#cite_ref-6)** Owen Byer; Felix Lazebnik; [Deirdre L. Smeltzer](/source/Deirdre_Smeltzer) (19 August 2010). [*Methods for Euclidean Geometry*](https://books.google.com/books?id=W4acIu4qZvoC&pg=PA53). MAA. pp. 53–. [ISBN](/source/ISBN_(identifier)) [978-0-88385-763-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-88385-763-2). Retrieved 2011-11-13.

1. **[^](#cite_ref-7)** Gerard Venema, "Exploring Advanced Euclidean Geometry with GeoGebra", MAA, 2013, p. 56.

1. ^ [***a***](#cite_ref-Josefsson_8-0) [***b***](#cite_ref-Josefsson_8-1) Josefsson Martin (2013). ["Five Proofs of an Area Characterization of Rectangles"](https://web.archive.org/web/20160304001152/http://forumgeom.fau.edu/FG2013volume13/FG201304.pdf) (PDF). *Forum Geometricorum*. **13**: 17–21. Archived from [the original](http://forumgeom.fau.edu/FG2013volume13/FG201304.pdf) (PDF) on 2016-03-04. Retrieved 2013-02-08.

1. **[^](#cite_ref-9)** [An Extended Classification of Quadrilaterals](http://mysite.mweb.co.za/residents/profmd/quadclassify.pdf) [Archived](https://web.archive.org/web/20191230004754/http://mysite.mweb.co.za/residents/profmd/quadclassify.pdf) 2019-12-30 at the [Wayback Machine](/source/Wayback_Machine) (An excerpt from De Villiers, M. 1996. *Some Adventures in Euclidean Geometry.* University of Durban-Westville.)

1. **[^](#cite_ref-10)** de Villiers, Michael, "Generalizing Van Aubel Using Duality", *Mathematics Magazine* 73 (4), Oct. 2000, pp. 303–307.

1. **[^](#cite_ref-11)** ["Rectangle"](https://www.mathsisfun.com/geometry/rectangle.html). *Math Is Fun*. Retrieved 2024-03-22.

1. **[^](#cite_ref-12)** [Cyclic Quadrilateral Incentre-Rectangle](http://math.kennesaw.edu/~mdevilli/cyclic-incentre-rectangle.html) [Archived](https://web.archive.org/web/20110928154652/http://math.kennesaw.edu/~mdevilli/cyclic-incentre-rectangle.html) 2011-09-28 at the [Wayback Machine](/source/Wayback_Machine) with interactive animation illustrating a rectangle that becomes a 'crossed rectangle', making a good case for regarding a 'crossed rectangle' as a type of rectangle.

1. **[^](#cite_ref-13)** Hall, Leon M. & Robert P. Roe (1998). ["An Unexpected Maximum in a Family of Rectangles"](https://web.archive.org/web/20100723134734/http://web.mst.edu/~lmhall/Personal/HallRoe/Hall_Roe.pdf) (PDF). *Mathematics Magazine*. **71** (4): 285–291. [doi](/source/Doi_(identifier)):[10.1080/0025570X.1998.11996653](https://doi.org/10.1080%2F0025570X.1998.11996653). [JSTOR](/source/JSTOR_(identifier)) [2690700](https://www.jstor.org/stable/2690700). Archived from [the original](http://web.mst.edu/~lmhall/Personal/HallRoe/Hall_Roe.pdf) (PDF) on 2010-07-23. Retrieved 2011-11-13.

1. **[^](#cite_ref-14)** Lassak, M. (1993). "Approximation of convex bodies by rectangles". *Geometriae Dedicata*. **47**: 111–117. [doi](/source/Doi_(identifier)):[10.1007/BF01263495](https://doi.org/10.1007%2FBF01263495). [S2CID](/source/S2CID_(identifier)) [119508642](https://api.semanticscholar.org/CorpusID:119508642).

1. **[^](#cite_ref-15)** [Sloane, N. J. A.](/source/Neil_Sloane) (ed.). ["Sequence A366185 (Decimal expansion of the real root of the quintic equation x 5 + 3 x 4 + 4 x 3 + x − 1 = 0 {\displaystyle \ x^{5}+3x^{4}+4x^{3}+x-1=0} )"](https://oeis.org/A366185). *The [On-Line Encyclopedia of Integer Sequences](/source/On-Line_Encyclopedia_of_Integer_Sequences)*. OEIS Foundation.

1. **[^](#cite_ref-16)** [Stars: A Second Look](https://web.archive.org/web/20150723004135/http://mysite.mweb.co.za/residents/profmd/stars.pdf). (PDF). Retrieved 2011-11-13.

1. ^ [***a***](#cite_ref-BSST_17-0) [***b***](#cite_ref-BSST_17-1) R.L. Brooks; C.A.B. Smith; A.H. Stone & W.T. Tutte (1940). ["The dissection of rectangles into squares"](http://projecteuclid.org/euclid.dmj/1077492259). *[Duke Math. J.](/source/Duke_Mathematical_Journal)* **7** (1): 312–340. [doi](/source/Doi_(identifier)):[10.1215/S0012-7094-40-00718-9](https://doi.org/10.1215%2FS0012-7094-40-00718-9).

1. **[^](#cite_ref-18)** J.D. Skinner II; C.A.B. Smith & W.T. Tutte (November 2000). ["On the Dissection of Rectangles into Right-Angled Isosceles Triangles"](https://doi.org/10.1006%2Fjctb.2000.1987). *[Journal of Combinatorial Theory, Series B](/source/Journal_of_Combinatorial_Theory%2C_Series_B)*. **80** (2): 277–319. [doi](/source/Doi_(identifier)):[10.1006/jctb.2000.1987](https://doi.org/10.1006%2Fjctb.2000.1987).

1. **[^](#cite_ref-19)** [Sloane, N. J. A.](/source/Neil_Sloane) (ed.). ["Sequence A219766 (Number of nonsquare simple perfect squared rectangles of order n up to symmetry)"](https://oeis.org/A219766). *The [On-Line Encyclopedia of Integer Sequences](/source/On-Line_Encyclopedia_of_Integer_Sequences)*. OEIS Foundation.

1. **[^](#cite_ref-20)** ["Squared Squares; Perfect Simples, Perfect Compounds and Imperfect Simples"](http://www.squaring.net/sq/ss/spss/o21/spsso21.html). *www.squaring.net*. Retrieved 2021-09-26.

1. **[^](#cite_ref-21)** R. Sprague (1940). "Ũber die Zerlegung von Rechtecken in lauter verschiedene Quadrate". *[Journal für die reine und angewandte Mathematik](/source/Crelle's_Journal)* (in German). **1940** (182): 60–64. [doi](/source/Doi_(identifier)):[10.1515/crll.1940.182.60](https://doi.org/10.1515%2Fcrll.1940.182.60). [S2CID](/source/S2CID_(identifier)) [118088887](https://api.semanticscholar.org/CorpusID:118088887).

## External links

Wikimedia Commons has media related to [Rectangles](https://commons.wikimedia.org/wiki/Category:Rectangles).

- [Weisstein, Eric W.](/source/Eric_W._Weisstein) ["Rectangle"](https://mathworld.wolfram.com/Rectangle.html). *[MathWorld](/source/MathWorld)*.

- [Definition and properties of a rectangle](https://www.mathopenref.com/rectangle.html) with interactive animation.

- [Area of a rectangle](https://www.mathopenref.com/rectanglearea.html) with interactive animation.

v t e Polygons (List) Triangles Acute Equilateral Ideal Isosceles Kepler Obtuse Right Quadrilaterals Antiparallelogram Apollonius Bicentric Crossed Cyclic Equidiagonal Ex-tangential Harmonic Isosceles trapezoid Kite Orthodiagonal Parallelogram Rectangle Right kite Right trapezoid Rhomboid Rhombus Square Tangential Tangential trapezoid Trapezoid By number of sides 1–10 sides Monogon (1) Digon (2) Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6) Heptagon/Septagon (7) Octagon (8) Nonagon/Enneagon (9) Decagon (10) 11–20 sides Hendecagon (11) Dodecagon (12) Tridecagon (13) Tetradecagon (14) Pentadecagon (15) Hexadecagon (16) Heptadecagon (17) Octadecagon (18) Icosagon (20) >20 sides Icositrigon (23) Icositetragon (24) Triacontagon (30) 257-gon Chiliagon (1000) Myriagon (10,000) 65537-gon Megagon (1,000,000) Apeirogon (∞) Star polygons Pentagram Hexagram Heptagram Octagram Enneagram Decagram Hendecagram Dodecagram Classes Concave Convex Cyclic Equiangular Equilateral Infinite skew Isogonal Isotoxal Magic Pseudotriangle Rectilinear Regular Reinhardt Simple Skew Star-shaped Tangential Weakly simple

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Adapted from the Wikipedia article [Rectangle](https://en.wikipedia.org/wiki/Rectangle) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Rectangle?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.