Rectangle

Pronunciation: /ˈrɛkˌtæŋ.gəl/ Explain

Click on the blue points and drag them to change the figure.

Can a rectangle also be a square?
Manipulative 1 - Rectangle Created with GeoGebra.

A rectangle is a quadrilateral (four sided figure) with vertices that make right angles.[1]

Properties of Rectangles

  • All rectangles have four sides.
  • The corners of rectangles are right angles
  • Opposite sides of a rectangle are congruent.
  • Opposite sides of a rectangle are parallel.
  • The diagonals of a rectangle are congruent.
  • The diagonals of a rectangle bisect each other.
  • All squares are also rectangles.
  • A rectangle is also a parallelogram.

Formulas for a Rectangle

Given the length (l) and width (w) of a rectangle:

FormulaDescription
A = l·wThe area of a rectangle is the length times the width.
P = 2·(l + w)The length of the perimeter of a rectangle is twice the length plus the width.
length of a diagonal = square root( l^2 + w^2 )The length of a diagonal of a rectangle is the square root of the length squared plus the width squared. This is derived using the Pythagorean Theorem.
Table 1: Formulas of a rectangle.

Tessellations of Rectangles

Tessellations of rectangles are found in many applications, including brick laying. Table 2 shows six tessellations of rectangles.

Tessellation of rectangles in the basket weave 1 form. Tessellation of rectangles in the basket weave 2 form. Tessellation of rectangles in the herring bone form.
Basket weave 1 Basket weave 2 Herring bone
Tessellation of rectangles in the running bond form. Tessellation of rectangles in the stack bond form. Tessellation of rectangles in the subway form.
Running Bond Stack Bond Subway

References

  1. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 29. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/4/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/29/mode/1up. Buy the book
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 77. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 12/4/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/77/mode/1up/search/rectangle. Buy the book

Educator Resources

  • McAdams, David E.. Rectangle Worksheet. lifeisastoryproblem.com. 3/15/2010. http://www.lifeisastoryproblem.com/worksheets/rectangle01.pdf.

Cite this article as:

McAdams, David E. Rectangle. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/rectangle.html.

Image Credits

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
8/28/2018: Corrected spelling. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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