How many triangles are there in the given figure?

32

The logic followed here is;

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

1+2= 03  (ARB) 

1+2= 03  (BRF)

1+2= 03  (ERF)

1+2= 03  (ARE)

1+2= 03  (CSD)

1+2= 03  (DSH)  

1+2= 03  (GSH)

1+2= 03  (CSG)

And, the other triangles are;

ABF, AEF, AEB, FEB, CDH, CGH, CDG, HGD

Therefore, there are 03+03+03+03+03+03+03+03+08= 32 triangles in the above figure