Question

please help. me solve this problem

Answer 1

Construction :- Join points B and D.Since X and Y are the mid points of sides BC and CD respectively,In ∆BCD, XY|| BD and XY = BD.⇒ ar (∆CYX) =   1/4ar (∆DBC)⇒ ar (∆CYX) = 1/8  ar (||gm ABCD)[Area of parallelogram is twice the area of triangle made by the diagonal]Since parallelogram ABCD and ∆ABX are between the same parallel lines AD and BC and BX =1/2 BC.ar (∆ABX) = 1/4  ar (||gm ABCD)Similarly, ar (∆AYD) =  ar (||gm ABCD)Now, ar (∆AXY) = ar (||gm ABCD) – [ar (∆ABX) + ar (∆AYD) + ar (∆CYX)] ar (||gm ABCD) -  ar1/4(llgm ABCD) +1/4 ar (||gm ABCD) + 1/8 ar (||gm ABCD)]
=area(llgm ABCD)-5/8(llgm ABCD)
=3/8(ll gm ABCD)