CLASS-9
AREA OF RHOMBUS

                               1

      Area of a Rhombus = ------ X Product of its diagonals 

                               2

                                 1

                          =  (------ X d₁ X d₂) sq.units

                                 2                                                                                                                  

Please note – The diagonals of a rhombus bisects each other at right angles.

Example.1) The diagonals of a rhombus are 40 cm and 32 cm.

Find, i) the area of rhombus, and

ii) perimeter of rhombus

Ans.)  i) As per the formulae –

                         1

Area of rhombus = ------- X Product of its diagonals

                         2

                         1

                   = ------- X 40 X 32 = 640 cm²

                         2

ii) we know that the diagonals of a rhombus bisects each other at right angles.

From above diagram, we find -

AO = OC = 20 cm, BO = OD = 16 cm, and ∠AOB = 90ᵒ           

By, Pythagoras theorem, we have –

AB = √(AO)² + (BO)² = √(20)² + (16)

                        =  √(400 + 256) = √656 = 25.61 cm            

So, the perimeter of the rhombus = 4 X 25.61 = 102.44 cm   (Ans.)