Explanation

For an n-sided polygon, the number of triangles using exactly one side of the polygon is n(n−4): choose one of the n sides, and the third vertex must be one of the n−4 vertices not adjacent to either endpoint. With n = 8, this gives 8 × 4 = 32. (Check: C(8,3) = 56 total triangles, minus 8 using two sides and 16 using none, leaves 32.)