# Square

## 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 opposite vertices of the square. As we have four vertices of a square, thus we can have two diagonals within a square. Diagonals of the square are always greater than its sides.

Below given are some important relation of diagonal of a square and other terms related to square.

• Relation between Diagonal ‘d’ and side ‘a’ of a square
$d = a \sqrt{2}$
• Relation between Diagonal ‘d’ and Area ‘A’ of a Square-
$d = \sqrt{2A}$
• Relation between Diagonal ‘d’ and Perimeter ‘P’ of a Square-
$d = \frac{P}{2 \sqrt {2}}$
• Relation between Diagonal ‘d’ and Circumradius ‘R’ of a square:
d = 2R
• Relation between Diagonal ‘d’ and diameter of the Circumcircle:$d = D_{c}$
• Relation between Diagonal ‘d’ and In-radius (r) of a circle-
$d = 2\sqrt {2}r$
• Relation between Diagonal ‘d’ and diameter of the In-circle-
$d = \sqrt {2}D_{i}$
• Relation between diagonal and length of the segment l-
$d = l \frac{2\sqrt {10}}{5}$

Properties of a 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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