Q. 84.4( 7 Votes )

ABCD is a

Answer :

Construction: Draw FG perpendicular to AB.



Proof: We have,


BE = 2 EA


And,


DF = 2FC


AB - AE =2 AE


And,


DC - FC = 2 FC


AB = 3 AE


And,


DC = 3 FC


AE = AB and FC = DC (i)


But,


AB = DC


Then,


AE = FC (Opposite sides of a parallelogram)


Thus,


AE || FC such that AE = FC


Then,


AECF is a parallelogram


Now, Area of parallelogram (AECF) = (AB × FG) [From (i)


3 Area of parallelogram AECF = AB × FG (ii)


And,


Area of parallelogram ABCD = AB × FG (iii)


Compare equation (ii) and (iii), we get


3 Area of parallelogram AECF = Area of parallelogram ABCD


Area of parallelogram AECF = Area of parallelogram ABCD


Hence, proved


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