Question

Prove that the area of a rhombus is half the product of its diagonals. Irritating answers will be reported!
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Answer 1

NICE QUESTION

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

Then ∠AOD=∠AOB=∠COD=∠BOC=90 degree

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)+1/2OC(BO+OD)

=1/2×AO×BD+1/2×OC×BD

=1/2BD(AO+OC)=1/2×BD×AC

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

Step-by-step explanation:

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