ABCD is a parallelogram. X and Y are the midpoints of BC and CD. Find

1.	ABCD is a parallelogram. X and Y are the midpoints of BC and CD. Find the ratio of ar (AAXY)to ar (llgm ABCD).22.
Answer» Given that ABCD ia a parallelogram. 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 CYX= 1/4 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} IMPLIES AREA TRIANGLE CYX= 1/8 parallelogram ABCD [Area parallelogram is twice the area of triangle made by the diagonal] Since parallelogram 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 AYD= 1/4 area parallelogram ABCD Now, area triangle AXY= area/parallelogram ABCD- {ar triangleABX + ar AYD + ar CYX} = parallelogramABCD - {1/4 + 1/4 + 1/8} area of parallelogram =area of parallelogram- 5/8 area parallelogram ABCD =3/8 area /parallelogram ABCD.

ABCD is a parallelogram. X and Y are the midpoints of BC and CD. Find the ratio of ar (AAXY)to ar (llgm ABCD).22.

Answer»

Given that ABCD ia a parallelogram. 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 CYX= 1/4 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}

IMPLIES AREA TRIANGLE CYX= 1/8 parallelogram ABCD

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

Since parallelogram 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 AYD= 1/4 area parallelogram ABCD

Now, area triangle AXY= area/parallelogram ABCD- {ar triangleABX + ar AYD + ar CYX}

= parallelogramABCD - {1/4 + 1/4 + 1/8} area of parallelogram

=area of parallelogram- 5/8 area parallelogram ABCD

=3/8 area /parallelogram ABCD.