How many triangles are in this image?

[68charger440]

I kept losing count at 41

You should get stuck at 40 unless you start using the lines and white space creatively.
There are 10 on each row otherwise.

[XH29N0G]

I kept losing count at 41

My guess is the 41 comes from double counting the big one. 

I counted that one (1), then the (4+4+4+4) one across, (4+4+4) two across, (4+4) three across and then the (4) four across without recognizing that the largest 4 across was also the big one.