Question

ABCD is a parallelogram. X and Y are mid-points of BC and CD respectively. Prove that
area (AAXY) = 3/8 area (parallelogram ABCD).
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Answer 1

Answer:

Give that ABCD is a // gm. X and Y are the mid points of BC and CD

Construction: Join BD

Since X and Y are the mid points of sides BC and CD respectively, therefore in triangle BCD, XY//BD and XY = 1/2 BD

Implies area of triangle DBC

{In triangle BCD, if X is the mid point of BC and Y is the mid pt of CD then area triangle CYX= 1/4 area triangle DBC}

IMOLIES AREA TRIANGLE CYX=1/8 area // gm ABCD

[Area of//gm is twice the area of triangle made by the diagonal]

Since// gm ABCD and triangle ABX are between same // lines AB and BC and BX=1/2BC

Therefore, area triangle ABX=1/4 area //gm ABCD

Similarly, area triangle ABX=1/4 area//gm ABCD

Now, area triangle AXY =area//gm ABCD- {ar triangle ABX+ar AYD ar CYX}

=ar//gm ABCD-{1/4 + 1/4 + 1/8} area// gm ABCD

=area // gm ABCD-5/8 area// gm ABCD

=3/8 area//gm ABCD.

Step-by-step explanation:

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