Chapter 9, Problem 9.9PE

(Geometry: n-sided regular polygon) In an n-sided regular polygon, all sides have the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). Design a class named RegularPo1ygon that contains:

• A private int data field named n that defines the number of sides in the polygon with default value 3.
• A private doub1e data field named side that stores the length of the side with default value 1.
• A private doub1e data field named x that defines the x-coordinate of the polygon's center with default value 0.
• A private doub1e data field named y that defines the y-coordinate of the polygon's center with default value 0.
• A no-arg constructor that creates a regular polygon with default values.
• A constructor that creates a regular polygon with the specified number of sides and length of side, centered at (0, 0).
• A constructor that creates a regular polygon with the specified number of sides, length of side, and x- and y-coordinates.
• The accessor and mutator methods for all data fields.
• The method getPerimeter () that returns the perimeter of the polygon.
• The method getArea () that returns the area of the polygon. The formula for computing the area of a regular polygon is

  $Area=\frac{n\times s^2}{4\times \tan \left(\frac{\pi }{n}\right)}$

Draw the UML diagram for the class then implement the class. Write a test program that creates three RegularPolygon objects, created using the no-arg constructor, using RegularPolygon ( 6 , 4) , and using RegularPolygon ( 10 , 4 , 5 . 6 , 7 . 8) . For each object, display its perimeter and area.