Question

Prove that the area of a rhombus is equal to half the area of the rectangle contained by its diagonals.

Answer 1

GIVEN :-

⇒ ABCD is a Rhombus.

⇒Diagonals of Rhombus are AC and BD.

⇒ AO is perpendicular to BD.

TO PROVE ;-

⇒ Ar . of the rectangle = L x B = AC × BD = d1 x d2

PROOF ;-

⇒ The diagonals of the rhombus are the length and breadth of a rectangle, and therefore we can take this diagonals as the length and breadth of the rectangle.
 

So,

⇒ Area of rectangle = l  ×  b

                   

                                     ⇒Length of rectangle  =  d 1

                                     ⇒ Breadth of rectangle = d  2

⇒Therefore,

                           ⇒ Ar. of rectangle = l × b
     
                                                      =  AC × BD
               
                                                      = d1   × d2

Hence proved

Answer 2

Step-by-step explanation:

hence proved

ok bye. it is easy or tough

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