## Definition

It is a geometric shape having four equal line segments that intersect at four points to create four internal angles of 90° each.

## Properties

- All four interior angles are right angles; in □ ABCD, ∠ABC = ∠BCD = ∠CDA =∠DAB = 90°
- Has four vertices and four sides; A, B, C and D are vertices and AB, BC, CD and DA are sides
- All four sides are congruent; so AB ≅ BC ≅ CD ≅DA
- Opposite sides are parallel to each other; AB ∥ CD and BC ∥ DA
- Diagonals of the square bisect each other at 90°
- Two diagonals of the square are perpendicular to each other; AC = BD

## Formulas

### Diagonal

The segment that connects two
opposite vertices of the square at right-angle to each other. The formula is
given below:

**Problem**: Finding the diagonal of a square when only the **SIDES** are known

**Find the diagonal of a square whose sides measure 4 cm.**

Solution:

As we know,

**Diagonal (***d*) = *a *× √2, where *a* = 4 cm

= 4 x √2 cm

= 5.656 cm

### Area

The total space enclosed by the
square. The formula is given below:

**Problem**: Finding the area of a square when only the **SIDES** are known

**Find the area of a square whose sides measure 6 cm.**

Solution:

As we know,

**Area (***A*) = *a*^{2}, where *a* = 6 cm

= 6 x 6 cm^{2}

= 36 cm^{2}

### Perimeter

The total distance covered around the edge of the square. The
formula is given below:

**Problem**: Finding the perimeter of a square when only the **SIDES** are known

**Find the perimeter of a square whose sides measure 10 cm.**

Solution:

As we know,

**Perimeter (***P* ) = 4*a*,where a = 10 cm

= 4 x 10 cm

= 40 cm