How many triangles are there in the given figure?

19

The logic followed here is;

(let's keep in mind the base, means how many triangles are there in the base)

1+2= 03  (FOG) 

1+2= 03  (DOE)

1+2= 03  (FOD) 

1+2= 03  (GOE)

And, the other triangles are;

FEG, FED, FGD, GDE, FBD, AFG, CGE

Therefore, there are 03+03+03+03+07= 19 triangles in the above figure.