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Question


In the figure given above, the ratio Area of DPQCArea of ABCD =____.
  1. 12
  2. 23
  3. 13
  4. 1


Solution

The correct option is B 23

Let h be the height between the parallel lines AB and CD

PQ=13AB

Hence, area of DPQC = 12×h times(PQ+DC)
 
           = h2×(DC+AB3)
 
           = h2×(DC+DC3)
  
           = h2×(4DC3)
 
           =2h×DC3

Now, we know that h×DC= area of parallelogram ABCD

Hence, area of trapezium DPQC = 23× area of parallelogram ABCD

Thus,Area of DPQCArea of ABCD=23
 

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