Question

abcd is a llgm x and y are the mid point of bc and cd

to prove
ar(axy)= 3/8(ar abcd)

Answer 1

i didnt understand q plzz ex0lain it properly

Answer 2

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 =1/2 BD.
⇒ ar (∆CYX) =  1/4ar (∆DBC)
⇒ ar (∆CYX) =  1/8ar (||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 = 1/2BC.
ar (∆ABX) =  1/4ar (||gm ABCD)
Similarly, ar (∆AYD) = 1/4 ar (||gm ABCD)
Now, ar (∆AXY) = ar (||gm ABCD) – [ar (∆ABX) +ar (∆AYD) +ar (∆CYX)]
 ar llgm ABCD - 1/4ar (||gm ABCD) +1/4  ar (||gm ABCD) + 1/8 ar (||gm ABCD)]
=ar llgm ABCD - 5/8 llgm ABCD
=3/8 llgm ABCD