# 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.

## Formulas

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

= 2 plotted on

*Cartesian coordinates*.

## Related pages

## References

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