How many equilateral triangles of side 1 are there in an irregular hexagon?

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As the question states, given a hexagon whose sides are not necessarily equal, but all the angles of this hexagon are equal to 120 degrees, how many equilateral triangles of side 1 can fit inside that hexagon?

Please, refer to the pictures for clarification.

Hexagon with 6 triangles

Hexagon with 13 triangles