join A and D to get AD median
Median divides the triangle into 2 triangles of equal area
therefore, ar(ABD)=1/2 ar(ABC)
now, join A and E to get AE median
Similarly we can prove that ar(ABE) = 1/2 ABD
==> ar(ABE)= 1/4 ABC [ because ar(ABD)= 1/2 ar(ABC) ] ---------1)
Join B and O and we get BO median
Now, ar(BOE)= 1/2 ar(ABE)
==>ar(BOE)= 1/2 x 1/4 ar(ABC)
==>ar(BOE)= 1/8 ar(ABC)