Square – Properties – Formula

Here we will learn, about some geometrical properties of a square.

In below figure ABCD is a square.

Properties of a square

1. All four sides of a square are equal or congruent.

1. All four sides of a square are equal or congruent.

AB  =  BC  =  CD  =  DA

2. All four angles of a square are equal, each angle of a square measures 90 degree.

∠ABC  =  ∠BCD   =  ∠CDA  =   ∠DAB  =  90⁰

3. Opposite sides are parallel and equal.

AB = DC and AD = BC

4. A square has two diagonals which are equal in length. 

AC and BD are diagonals and AC = BD

Diagonals AC and BD bisect each other at point o.

AC and BD are perpendicular to each other.

5. Area of △AOB = Area of △BOC = Area of △COD = Area of △DOA

6. Any two adjacent angles add up to 180 degrees.

7. Each diagonal bisect each other.

8. Diagonals bisect (divide in two equal angles) the pair of opposite angles. 

                          ∠DAC  =  ∠CAB

                          ∠ABD  =  ∠DBC

                          ∠BCA  =  ∠ACD

                          ∠CDB  =  ∠BDA

9. Both diagonals are perpendicular to each other or bisect each other at 90⁰ or right angles.

10. A square has four line of symmetry.

11. Each diagonals divides the square into two congruent isosceles right angled triangles.

12. The sum of four interior angles is four right angles.

13. The sum of four exterior angles is four right angles.

Square Formula

Perimeter of a square (P) = 4 x side

Area of a square (A) = (side)²

Diagonal of a square = √2 x side

Side of a square =√A = P/