__Introduction__**:**

It is often necessary to determine the dimensions of a regular polygon inscribed in or circumscribed about a given circle, or to determine the size of a circle that can be inscribed in or circumscribed about a given polygon. Such problems are readily solved by trigonometry and some of them may be solved by geometry. The practical applications of polygons are the gears.

__Regular Polygon__**:**

A plane figure bounded by a number of straight lines is called a **polygon**. A **regular polygon** is the one in which all sides and all the internal angles are equal. A regular polygon has a point , inside it, called its **center** which is equidistant from all its vertices and sides. A **convex polygon** is the one in which no angle is greater than two right angles, i.e. its has no reflex or re-entrant angle. (Regular polygons are convex polygons). From the above definitions, triangles and quadrilaterals are also polygons but generally we define the polygon as the figure bounded by more than four straight lines. The sum of the bounding sides of the polygon is called the **perimeter** of the polygon.