How many maximum triangles are there in the given figure?

28

The logic followed here is;

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

1+2= 03  (ALC) 

1+2= 03  (BMD)

1+2= 03  (ANQ) 

1+2= 03  (ABQ) 

1+2= 03  (NCD)

1+2= 03  (NQD) 

And, the other triangles are;

ANB, NQB, NCQ, CDQ, AQC, BND, NOQ, NPQ, ALQ, BMN

Therefore, there are 03+03+03+03+03+03+10= 28 triangles in the above figure.