Question

in triangle abc ,d and e are mid points of ab and ac show that area of triangle ade =1/4area of triangle abc

Answer 1

the line segment joining the midpoint of any two side is parallel to the third side and is equal to half of it.
area of triangle ABC= 1/2*BC*Af (where Af is the median )
if you consider the midpoint of side BC as f you will find vertex A and point f is joined by median such that dAef forms a parallelogram where de and Af bisect each other 
. 
. . area of triangle Ade= 1/2* de *Ao
= 1/2*(1/2BC) * (1/2 Af)
= 1/4* area of triangle ABC