Find the ratio of areas

i hav a very cheecky method for this one....that is through cordinates.....

assume B to be origin

a be length of sides

let BC be along x axis

cordinates of c will be (a,0)

similrly for A will be (a/2,√3a/2)

now since we know that points F D E divide lines AB ,BC,CA in some ration (that we can find) find respective cordinates of D F and E....

then find eq of lines AD BE CF

find points of intersection of des lines to find cordinates of traingle of shaded traingle

and hence the area

i know this is lenghty

but is samay yehi aya dimag mey.......[3]