Regular polygon with $n$ sides , the number of triangles

73 Views Asked by At

For a regular polygon with $n$ sides $(n>5)$, the number of triangles whose vertices are joining non-adjacent vertices of the polygon is $n(n-4)(n-5)$.

When I take $n=6$, I get David's Star:

David's star:

So, only two triangles! How can I get $n(n-4)(n-5)$?