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A square and its diagonals
Drawing a square

A square is a shape with four equal sides and four corners that are all right angles (90 degrees). The diagonals of a square also cross at right angles. The angle between any diagonal and a side of a square is 45 degrees. A square has rotational symmetry of four. It has four lines of regular symmetry. A square with vertices A, B, C and D can be written as [math]\displaystyle{ \square ABCD }[/math].[1][2]

A square is a type of rectangle with all sides of equal length. However, while a square is a type of rectangle and rhombus,[3] the opposite does not need to be true.

A square is also the 2-dimensional analogue of a cube.


If the length of side a is known, then we have that:[2]

Perimeter [math]\displaystyle{ 4a }[/math]
Area [math]\displaystyle{ a^2 }[/math]
Length of diagonal [math]\displaystyle{ \sqrt{2}a }[/math]

If the length of diagonal d is known, then we have that:

Length of side [math]\displaystyle{ \frac{d}{\sqrt{2}} }[/math]
Perimeter[4] [math]\displaystyle{ 2d\sqrt{2} }[/math]
Area[4] [math]\displaystyle{ \frac{d^2}{2} }[/math]

Square Media

Related pages


  1. "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-02.
  2. 2.0 2.1 Weisstein, Eric W. "Square". mathworld.wolfram.com. Retrieved 2020-09-02.
  3. "Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram". www.mathsisfun.com. Retrieved 2020-09-02.
  4. 4.0 4.1 "Square. Formulas and Properties of a Square". onlinemschool.com. Retrieved February 17, 2018.