Question

Prove that the area of a rhombus is equal to half of the product of the diagonals.
E SAM​

Answer 1

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

= 1/2×AO×OD+1/2×AO×OB+ 1/2×BO×OC+ 1/2*OD×OC

=1/2*AO(OD+OB)+1/2*OC(BO+OD)

=1/2×AO×BD+1/2×OC×BD

=1/2*BD(AO+OC)=1/2×BD×AC

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

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