Triangle Puzzles

Okay so now it’s time to get serious. In this puzzle you can find 128 triangles just by counting the individual triangles but, as you will know by now, there are many more. How many do you reckon altogether —  362   408   546  or  628 ?

Puzzle 4

It might be fun to ask other people for their ideas before you see see the answer.

I have given a full explanation of the count to convince everyone that the number is correct!