Question

In triangle DEF, M and N are mid-points of sides EF and DE repectively. IF ar(EMN) = 4 cm^2. find ar( DEF). ​Don 't give link of similar query if give then only of this otherwise answer it.

Answer 1

mark the mid point of FD,as O
by M.P.T-MN=1/2 FD=FO
also,NO=MF............M.P.T
so,MNOF= llgm
so, MO=diagonal
so,ar(MFO)=ar(MNO)........diagonal of a llgm divides it in 2 equal triangles 
similarly,ar(EMN)=ar(MNO)=ar(NOD)=ar(MFO)=4cm^2
since,ar(DEF)=ar(EMN)+ar(MNO)+ar(NOD)+ar(MFO)
                      =4(4cm^2)
therefore, ar(DEF)=16cm^2