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.

• A. twice
• B. thrice
• C. half
• D. one-third

Answer 1

The correct option is A 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) = $\frac{1}{2}$ Area(PDBQ) = $\frac{1}{4}$ Area(PQRS)

Similarly, Area(DCB) = $\frac{1}{2}$ Area(DBRS) = $\frac{1}{4}$ Area(PQRS)

Area(DABC) = Area(ADB) + Area(DCB) = $\frac{1}{2}$ Area(PQRS)

Area(PQRS) = 2 × Area(DABC)