In ∆ABC, D, E and F are the mid-points of sides BC,

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In ∆ABC, D, E and F are the mid-points of sides BC, CA and AB respectively. What is the area of quadrilateral BDEF ?

1. 1 rd of area of ∆ABC
  3
2. Half of the area of ∆ABC
3. 1 th of the area of ∆ABC
  4
4. None of these

Correct Option: B

D, E are the mid-points on BC and AC respectively.
∴ DE || BA Þ DE || BF
Similarly, FE || BD
∴ BDEF is a parallelogram.
Similarly, DCEF and AFDE are parallelograms.
∴ ∆BDF = ∆DEF
∆DCE = ∆DEF
and ∆AFE = ∆DEF
∴ ∆BDF = ∆DCE = ∆AFE = DDEF

⇒ ∆DEF =	1	∆ABC
	4

∴ Quadrilateral BDEF = 2 × DDEF
⇒ Quadrilateral BDEF

= 2 ×	1	∆ABC
	4

=	1	∆ABC
	2

1	rd of area of ∆ABC
3