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  (ALM) 

1+2= 03  (ANO)

And, the other triangles are;

ABC, APB, APC

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