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  (AOF) 

1+2= 03  (ACD)

1+2= 03  (ECD)

And, the other triangles are;

ACE, ABE, ADB, EOD, CPF, ACF, AFE, ACP, APD, ADE, COF

Therefore, there are 03+03+03+11= 20 triangles in the above figure.