Question

prove that area of rhombus = 1/2•product of the diagonal ​

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

hope it helps u