The answer depends on the size of the triangles relative to the size of the hexagon.
flippant answer: infinite
answer you are probably looking for: 6
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That would depend on which hexagon and what triangles. A small hexagon might not have room for any large triangles. A large hexagon will have room fro many small triangles.If you have a regular hexagon and connect the vertices you will have drawn six equilateral triangles
A 6 sided hexagon has 4 triangles
you can split a regular hexagon into 6 triangles
4 triangles make 1 hexagon. (easy way to find out how many triangles there are in a polygon- take number of sides of the polygon, subtract 2 from it, that's your answer!)
6