# 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 ${\displaystyle \square ABCD}$.[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 ${\displaystyle 4a}$ Area ${\displaystyle a^{2}}$ Length of diagonal ${\displaystyle {\sqrt {2}}a}$

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

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

## References

1. "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-02.
2. 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. "Square. Formulas and Properties of a Square". onlinemschool.com. Retrieved February 17, 2018.