How many triangles are there in the given figure ?

The logic followed here is;

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

1+2= 03  (ADE) 

1+2= 03  (ABE)

1+2= 03  (DFG)

1+2= 03  (DEG)

And, the other triangles are;

DCE, DFE, FEG

Therefore, there are 03+03+03+03+03= 15 triangles in the above figure.