Question

In Java:

(Area of a convex polygon)

A polygon is convex if it contains any line segment that connects two points of the polygon. Write a program that prompts the user to enter the number of points in a convex polygon, then enter the points clockwise, and display the area of the polygon.

Sample Run

Enter the number of points: 7

Enter the coordinates of the points:

-12 0 -8.5 10 0 11.4 5.5 7.8 6 -5.5 0 -7 -3.5 -5.5

The total area is 244.575

Class Name: Exercise11_15

Answer 1

import java.util.Scanner;

public class Exercise11_15 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        System.out.print("Enter the number of points: ");
        int numPoints = in.nextInt();
        double[] x = new double[numPoints];
        double[] y = new double[numPoints];
        System.out.println("Enter the coordinates of the points:");
        for (int i = 0; i < numPoints; i++) {
            x[i] = in.nextDouble();
            y[i] = in.nextDouble();
        }

        double area = 0;
        for (int i = 0; i < numPoints; i++) {
            area += x[i] * y[(i + 1) % numPoints] - y[i] * x[(i + 1) % numPoints];
        }
        area = Math.abs(area / 2);
        System.out.printf("The total area is %.3f\n", area);
    }
}