# 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.

### 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:

The area of a rectangle is the length times the width.
A = l · w
P = 2·(l + w)The length of the perimeter of a rectangle is twice the length plus the width. 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.   Basket weave 1 Basket weave 2 Herring bone   Running Bond Stack Bond Subway
1. McAdams, David E.. All Math Words Dictionary, rectangle. 2nd Classroom edition 20150108-4799968. pg 152. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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
3. 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.

McAdams, David E. Rectangle. 5/3/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/r/rectangle.html.

### Revision History

5/3/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)