How many triangles are there in the given figure?

28

The logic followed here is;

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

1+2= 03  (ADF) 

1+2= 03  (IDF)

1+2= 03  (BEF) 

1+2= 03  (EFI)

1+2= 03  (TLC)

1+2= 03 (CDE)

And, the other triangles are;

AFI, ADI, FIB, EBI, FCB, FCD, ABC, FDE, AIC, BIC, AIB, AFC, BFC

Therefore, there are 03+03+03+03+03+03+13= 28 triangles in the above figure.