Square

For other uses, see Square (disambiguation).

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 and its diagonals

Drawing a square

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 surface 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]	${\displaystyle {\frac {d^{2}}{2}}}$

Related pages

• Square (algebra)
• Square number
• Square root