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Question

If A, B, C, D are mid-points of sides of parallelogram PQRS, area of PQRS is always ________ the area of shape formed by joining A,B,C,D.
  1. thrice
  2. half
  3. one-third
  4. twice


Solution

The correct option is D twice

Draw a line joining D and B.

See that parallelogram PDBQ and triangle ADB are on same base and between same parallels PQ and DB.

Area(ADB) = 12 Area(PDBQ) = 14 Area(PQRS)

Similarly, Area(DCB) = 12 Area(DBRS) = 14 Area(PQRS)

Area(DABC) = Area(ADB) + Area(DCB) = 12 Area(PQRS)

Area(PQRS) = 2 × Area(DABC)

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