How many triangles are there in the given figure?

38

The logic followed here is;

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

1+2= 03  (ABE) 

1+2= 03  (BPE)

1+2= 03  (CPO) 

1+2= 03  (DPO)

1+2= 03  (BOC)

1+2= 03  (EOD)

1+2= 03  (CPD)

And, the other triangles are;

BCD, ECD, EPD, BPC, QCD, RCD, COS, DOS, BDO, ECO, BEC, EBD, ABP, AEP, BDE, OQD, ORC

Therefore, there are 03+03+03+03+03+03+03+17= 38 triangles in the above figure.