See figure on the left. (In a concave polygon, some diagonals will lie outside the polygon). The area of an irregular convex polygon can be found by dividing it into triangles and summing the triangle's areas. See Area of an Irregular Polygon. Regular Polygons are always convex by definition. See Regular Polygon Definition. read more
These properties apply to all regular polygons, whether convex or star. A regular n-sided polygon has rotational symmetry of order n. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. read more
The radius of the incircle is the apothem of the polygon. (Not all polygons have those properties, but triangles and regular polygons do). Breaking into Triangles. We can learn a lot about regular polygons by breaking them into triangles like this: Notice that: the"base" of the triangle is one side of the polygon. read more