Square (geometry)

For other uses, see Square (disambiguation).

A square and its diagonals.

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

• Area: w² where w represents the length of any side.
• Area: ½d² where d represents the length of the diagonal, meaning the length of the line segment from one corner of the square to another.
• Perimeter: 4w where w represents the length of any side.
• Perimeter: 4d÷sqrt(2) where d represents the length of the diagonal, and sqrt(n) means the square root of n.
• The diagonal is equal to the square root of two, multiplied by the length of any side.