What is a Square?

Square is a regular quadrilateral where all the four sides and angles are equal. All the four angles are right angles. It can also be defined as a rectangle where two adjacent sides have equal length.

Diagonal of square

It is a segment that connects two vertices of opposite angles of the square. Diagonals of the square are always greater than its sides.

- The formula of the square diagonal for sides of a square:

d = a·√2

- The formula of the square diagonal for the square area:

d = √2A

- The formula of the square diagonal for square perimeter:

d = | P |

2√2 |

- the formula of the square diagonal for circumradius:

d = 2R

- the formula of the square diagonal for the diameter of the circumcircle:

d = Dc

- the formula of the square diagonal for the inradius:

d = 2r√2

- the formula of the square diagonal for the diameter of the incircle:

d = Di√2

- the formula of the square diagonal for the length of the segment l

d = l | 2√10 |

5 |

Properties of Square

A square is a kind of rhombus which has equal sides and opposite equal angles. A parallelogram which has its opposite sides parallel, a quadrilateral which has its four-sided polygon, and a rectangle which has its opposite sides equal and has right-angles.

The diagonals of a square bisect each other at 90°

- The diagonals of a square bisect its angles.
- The opposite sides of a square are both parallel and equal in length.
- All the four angles of a square are equal.
- All the four sides of a square are equal.
- The diagonals of a square are equal.

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