State true or false.In the following figure,

ABCD
is a trapezium in which

AB||DC
is a trapezium in which and

DC=40
and cm, XY = 50 cm and

AB=60
cm, XY = 50 cm and cm. If X and Y are, respectively, the mid points of AD and BC, then

area

trap.DCYX
=
9

11

area

trap.XYBA
.
cm. If X and Y are, respectively, the mid points of AD and BC, then

Question

State true or false.In the following figure,

ABCD
 is a trapezium in which

AB||DC
 is a trapezium in which and

DC=40
 and  cm, XY = 50 cm and

AB=60
  cm, XY = 50 cm and  cm. If X and Y are, respectively, the mid points of AD and BC, then

area
    
     trap.DCYX
   =
    9
    
     11
   
   area
    
     trap.XYBA
   .
  cm. If X and Y are, respectively, the mid points of AD and BC, then

Accepted Answer

Given that,

ABCD
 is a trapezium in which

AB||DC
 and

DC=40
  cm, XY = 50 cm and

AB=60
  cm.  X and Y are, respectively, the mid points of AD and BC.Area of the trapezium

=
    1
    2
   
   ×sum of parallel sides×height
 Since, X and Y are the midpoint of DA and CB respectively, trapezium

DCXY
  and

ABYX
  are of the same height say

h
 .

Area of trapezium DCXY=
    1
    2
   
   ×(DC+XY)×h

=
    1
    2
   
   ×(40+50)×h

=
    1
    2
   
   ×90×h

=45h

Area of trapezium ABYX=
    1
    2
   
   ×(AB+XY)×h

=
    1
    2
   
   ×(60+50)×h

=
    1
    2
   
   ×110×h

=55h
   Therefore,

area of DCXY
    
     area of ABXY
   
   =
    
     45h
    
     55h

=
    9
    
     11

ar
    
     trap.DCYX
   =
    9
    
     11
   
   ar
    
     trap.XYBA
   .
 Hence, the statement is true.Therefore, option 1 is correct.

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