∆ODE and ∆OCB are similar. We know that sides of similar triangles are in the same ratio. OE : OB = 2 : 1 If two triangles are similar then the ratio of their areas is equal to the ratio of squares of their corresponding sides.
Equation can be written as,
OE2
OB2
=
AreaoftriangleODE
AreaoftriangleBCO
Area of ∆BCO = 4(Area of ∆ODE)
1
3
(Area of ∆ABC) = 4 (Area of triangle ∆ODE) (∵ area of ∆BCO =
1
3
area of ∆ ABC) Area of ∆ ABC = 12 (Area of ∆ ODE) ∆ODE : ∆ABC = 1 : 12