1. Write a Java program to simulate a die. A die has values of either 1, 2, 3, 4, 5 or 6 on the face. You should use the Math.Random() or the java.util.Random() class to generate the values on the die. The program should prompt the user to enter how many times the die should be rolled. The output should show the results of each roll along with the total number of times 1, 2, 3, 4, 5 or 6 occurred for all rolls and the total sum comprised of the sum of all rolls. Here is a sample run:

How many times do you want to roll the die? 10

Thank you! The die roll results for 10 rolls were: 2 3 4 5 3 2 6 2 1 6 The number of occurrences of each face were as follows:

1: 1 2: 3 3: 2 4: 1 5: 1 6: 2

The sum of die rolls was: 34

2. Design a Java class named Polygon that contains:

A private int data field named numSides that defines the number of sides of the polygon. The default value should be 4.
A private double data field named sideLength that defines the length of each side. The default value should be 10.0.
A private double data field named xCoord that defines the x-coordinate of the center of the polygon. The default value should be 0.0.
A private double data field named yCoord that defines the y-coordinate of the center of the polygon. The default value should be 0.0.
A no argument constructor that creates a Polygon using the default number of sides, default side length and default x- and y-coordinates.
A constructor that creates a Polygon using a specified number of sides, side length and x- and y-coordinates.
Getter and setter methods for all data fields

A getPerimeter() method that returns a double value representing the sum of all sides.

A toString() method that displays the number of sides, side length, x-coordinate and y-coordinate values in String format.

Be sure your code compiles. (In the next question, you will create a TestPolygon class and test each of the methods)

Write a Java test program, named TestPolygon, to create five different polygons. When creating the five polygons, create one using the no argument constructor. For the remaining four, feel free to use any number of sides, side length and x-, and y-coordinates that are not equal to the default values and not equal to each other. For each of the five polygons, call all of the methods and display the results. For example for a Polygon with 3 sides, side length of 2.0 and x-coordinate and y-coordinates of 1.0, the following output may be appropriate.

toString() results: (3, 2.0, 1.0,1.0) getNumSides() results: 3 getSideLength() results: 2.0 getXCoord() results: 0.0 getYCoord() results: 0.0 getPerimeter() results: 6.0 setNumSides(4) results: 4 setSideLength(3) results: 3.0 setXCoord(2.0) results: 2.0 setYCoord(2.0) results: 2.0

Keep in mind, for five Polygons, you will have five different output results. Also, note there is no requirement to actually draw a Polygon.