How Many Triangles Can Be Drawn by Joining the Vertices and the Center of a Regular Hexagon?

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Maths keeps one mentally active. In a hexagon there are 6 vertices. By joining the centre to eaxh of the vertices of a hexagon, one can form 6 acute triangles, 6 obtuse triangles, that is 12 in all.

How many triangles are in an 8 sided polygon?

The number of triangles is 1, 8, 35, 110, 287, 632, 1302, 2400, 4257, 6956 for polygons with 3 through 12 sides. Introduction. If we connect all vertices of a regular N-sided polygon we obtain a figure with = N (N – 1) / 2 lines. For N=8, the figure is: Careful counting shows that there are 632 triangles in this eight sided figure. Derivation