Question

area of aquadrilateral is the product of half of its diagonals proof

Answer 1

5636th 637737388287476477388

Answer 2

Step-by-step explanation:

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

Then ∠AOD=∠AOB=∠COD=∠BOC=900

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

=21×AO×OD+21×AO×OB+21×BO×OC+21×OD×OC

=21×AO(OD+OB)+21OC(BO+OD)

=21×AO×BD+21×OC×BD

=21BD(AO+OC)=21×BD×AC

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

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