Hi, I have a problem with java. Please help me with this question. Using recursi

Question

Hi, I have a problem with java. Please help me with this question.

Using recursion, write a program to compute the area of a polygon shown. You can use the vertices 1, 2, and 3 and cut off a triangle and use the fact that a triangle with points 1(x_1, y_1), 2(x_2, y_2), and 3(x_3, y_3) as corners, has an area of: area=(x_1y_2 + x_2y_3 + x_3y_1 - y_1x_2 - y_2x_3 - y_3x_1) Then move to vertices 1, 3, and 4 and do the area calculation. Continue with 1, 4, and 5 and then 1, 5, and 6 to do the same. You stop the recursion when you run out of triangles.

Explanation / Answer

/**
* The java program PolygonArea that calls the method polygonarea that
* prints the area of polygon formed by x and y array values
* */
//PolygonArea.java
public class PolygonArea {

   public static void main(String[] args) {   
       double[] x = {7.0, 15.0, 11.0, 4.0};
       double[] y = {12.0, 9.0, 2.0, 9.0};
       int i = 0;
       double area = 0;

       //print points of x and y arrays
       System.out.println("Polygon points: ");
       for (int index = 0; index < x.length; index++) {
           System.out.println("("+x[index]+","+y[index]+")");          
       }
      
       //calling polygonarea method
       area = polygonarea(x, y, i, area);
       System.out.println("Area of polygon :");
       System.out.println(area);

   }

   /**The method polygonarea takes arrays of double types, x and y
   * and returns the area of polygon */
   public static double polygonarea (double[] x, double[] y, int i, double area){       
       if (i == x.length-2){
           //return area value
           return Math.abs(area) ;
       } else{
           //find area of triangles formed by the points
           //add to area
           area += (x[0]*y[i+1] + x[i+1]*y[i+2] +
                   x[i+2]*y[0] - y[0]*x[i+1] -
                   y[i+1]*x[i+2] - y[i+2]*x[0])/2;
           //calling recursively
           return polygonarea(x, y, i+1, area);
       }

   }  
}

Sample output:

Polygon points:
(7.0,12.0)
(15.0,9.0)
(11.0,2.0)
(4.0,9.0)
Area of polygon :
55.0

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