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you have proved that ar( ABF ) = ar ( EAC )
2 ar ( ABF ) = ar (  ARHF ) ----------------(1)
( since they are on the same base and between the same parallel )
2 ar (EAC ) = ar ( ABDE ) ---------------(2)
comparing (1) and (2)
we get that
ar ( ARHF ) =ar ( ABDE )

i hope it helps.....................
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thank you
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