Square

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 $◻ABCD$.

A square is a type of rectangle with all sides of equal length. However, while a square is a type of rectangle and rhombus, 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:

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

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

Length of side	$\frac{d}{\sqrt{2}}$
Perimeter	$2d\sqrt{2}$
Area	$\frac{d^2}{2}$

Related pages

• Square (algebra)
• Square number
• Square root