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  (AOB) 

1+2= 03  (AMB)

1+2= 03  (ACM)

1+2= 03  (AOM)

And, the other triangles are;

COM, AOC, BOM, BMD, BCD, ACB, AOC, APC, CBM

Therefore, there are 03+03+03+03+09= 21 triangles in the above figure.