4.1
import java.util.Scanner; public class Welcome
{
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
System.out.print("Enter the length from the center to a vertex:");
double r = input.nextDouble();
double s = 2 * r * Math.sin(Math.PI / 5);
double area = 5 * s * s / (4 * Math.tan(Math.PI / 5));
System.out.printf("The area of the pentagon is %.2f",area);
}
}
4.2
import java.util.Scanner; public class Welcome
{
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
System.out.print("Enter point 1(latitude and longitude) in degrees:");
double deX1 = input.nextDouble(),deY1 = input.nextDouble();
System.out.print("Enter point 2(latitude and longitude) in degrees:");
double deX2 = input.nextDouble(),deY2 = input.nextDouble();
double x1 = Math.toRadians(deX1),y1 = Math.toRadians(deY1);
double x2 = Math.toRadians(deX2),y2 = Math.toRadians(deY2);
final double r = 6371.01;
double d = r * Math.acos(Math.sin(x1) * Math.sin(x2) + Math.cos(x1) * Math.cos(x2) * Math.cos(y1 - y2));
System.out.println("The distance between the two points is "+d+" km");
}
}
4.3
4.4
import java.util.Scanner; public class Welcome
{
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
System.out.print("Enter the side: ");
double s = input.nextDouble();
double area = 6 * s * s / (4 * Math.tan(Math.PI / 6));
System.out.printf("The area of the hexagon is %.2f",area);
}
}
4.5
import java.util.Scanner; public class Welcome
{
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
System.out.print("Enter the number of sides:");
int num = input.nextInt();
System.out.print("Enter the side:");
double s = input.nextDouble();
double area = num * s * s / (4 * Math.tan(Math.PI / num));
System.out.println("The area of the polygon is "+area);
}
}
4.6