Question

D is mid point of side BC of a triangle ABC and E is mid point of BD.If O is mid point of AE , then prove that ar(BOE)=1/8ar(ABC)

Answer 1

ar(ABD)=ar(ADC)    [Triangle on the same base and on between same parallel lines]...(1)
ar(ABE)=ar(AED)    [Triangle on the same base and on between same parallel lines] ....2
ar(BOE)=ar(BOA)  [Triangle on the same base and on between same parallel lines] ....3    now     
2 ar(ABD)=ar(ABC) from1
4ar(ABE)=ar(ABC) from2
8ar(BOE)=ar(ABC) from3  So;ar(BOE)=1/8ar(ABC) proved