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Squares (Mathematics Glossary)

What Is a Square?

A square is a four sided shape with four equal sides and four right angles.

Properties of Squares

  • All sides of a square are of equal length.


  • All angles in a square are right angles.


  • Opposite sides of a square are parallel.


  • All angles of a square add up to 360°.

  • The diagonals of a square bisect each other at right angles. The diagonals cross each other half-way along their lengths and are perpendicular to each other.

The Perimeter of a Square

The perimeter of a square is given by the formula:



where a is the length of the side of the square.

The Area of a Square

The area of a square is given by the formula:



where a is the length of the side of the square.
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Note

A SQUARE IS A POLYGON

A square is a type of polygon.

A polygon is a 2-dimensional shape with straight sides.

A square is a regular polygon. Regular polygons have the same length sides and the same angles.

A SQUARE IS A QUADRILATERAL

A square is a quadrilateral.

A square is a four-sided polygon.

Parallelograms, rectangles and trapezoids are also quadrilaterals.

SQUARE NUMBERS...

A square number is a number multiplied by itself.

12 = 1 × 1 = 1
22 = 2 × 2 = 4
32 = 3 × 3 = 9

The squares go 1, 4, 9...

A square with sides of length 1 has an area of 1.



A square with sides of length 2 has an area of 4.



A square with sides of length 3 has an area of 9.



The areas go 1, 4, 9...

The square of a number and the area of a square with side lengths of that number are the same.

... AND SQUARE ROOTS

A square root is the inverse of a square number.

If a number represented the area of a square, then the square root represents the length of the side of that square.