# Square

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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 is a type of rectangle with all sides of equal length. However note that while a square is a type of rectangle, a rectangle does not necessarily need to be a square.

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

## Formulas

If the length of side a is known:

 Perimeter ${\displaystyle 4a}$ Area ${\displaystyle a^{2}}$ Length of diagonal ${\displaystyle {\sqrt {2}}a}$

If the length of diagonal d is known:

 Length of side ${\displaystyle {\frac {d}{\sqrt {2}}}}$ Perimeter[1] ${\displaystyle 2d{\sqrt {2}}}$ Area[1] ${\displaystyle {\frac {d^{2}}{2}}}$

## References

1. "Square. Formulas and Properties of a Square". onlinemschool.com. Retrieved February 17, 2018.