Number of traingle with one side common with polygon
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The number of triangles is 1, 8, 35, 110, 287, 632, 1302, 2400, 4257, 6956 for polygons with 3 through 12 sides. 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.
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