Question

Answer this question fast with explanation.....I will mark the best answer as brainlist​

Answer 1

Answer:

Step-by-step explanation:

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 = 1/2 BD.

⇒ area (∆CYX) =  1/4 * area (∆DBC)

⇒ area  (∆CYX) =  1/8 * area  (||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.

area (∆ABX) =  1/4 area (||gm ABCD)

Similarly, area (∆AYD) =  1/4area (||gm ABCD)

Now, area (∆AXY) = area (||gm ABCD) - [area (∆ABX) + area (∆AYD) + area (∆CYX)]

  =  area (||gm ABCD) - [1/4 area (||gm ABCD) + 1/4 area (||gm ABCD) + 1/8 * area  (||gm ABCD) ]

= area (||gm ABCD) - 5/8 * area (||gm ABCD)

= 3/8 * area (||gm ABCD)