Cassandra is Playing with Polygons

Cassandra was gifted a regular polygon with $N$ vertices labelled from $1$ to $N$ in clockwise order. She was taught in school that the **triangulation** of a polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon and there is no pair of triangles such that they have any area in common and the total area of all triangles is equal to the area of the