`A B C D` is a parallelogram `X` and `Y` are the mid-points of `B C` and `C D` respectively. Prove that `a r( A X Y)=3/8a r(|\|^(gm)A B C D)` GIVEN : A parallelogram `A B C D` in which `X` and `Y` are the mid-points of `B C` and `C D` respectively. TO PROVE : `a r( A X Y)=3/8a r(|\|^(gm)a b c d)` CONSTRUCTION : Join `B Ddot`

Explanation

`In /_BCD`

X and Y are midpoint of sides BC and CD

XY||BD and XY=1/2BD

`ar(/_CXY)=1/4*ar(/_ABC)`

`ar(/_CYX)=1/8*ar(paral l elogram ABCD)-(1)`

ParallelogramABCD and `/_ABX`

AD||BX

`BX=1/2BC`

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