Question

Prove That Area Of Rhombus=1/2 (Product Of Parallelogram)

Answer 1

Answer:

Given ABCD is a rhombus the diagonal AC and BD cut at point O

Then ∠AOD=∠AOB=∠COD=∠BOC=90  

0

 

The area of rhombus ABCD divided diagonal in four parts  

So area of rhombus ABCD =area of triangle AOD+area of triangle AOB+area of triangle BOC+area of triangle COD

=  

2

1

​

×AO×OD+  

2

1

​

×AO×OB+  

2

1

​

×BO×OC+  

2

1

​

×OD×OC

=  

2

1

​

×AO(OD+OB)+  

2

1

​

OC(BO+OD)

=  

2

1

​

×AO×BD+  

2

1

​

×OC×BD

=  

2

1

​

BD(AO+OC)= 2

1

​

×BD×AC

So area of rhombus is equal to half of the product of diagonals

Step-by-step explanation: