4.1 (Geometry: area of a pentagon) Write a program that prompts the user to enter the length from the center of a pentagon to a vertex and computes the area of the pentagon, as shown in the following figure. The formula for computing the area of a pentagon is
, where s is the length of a side. The side can be computed using the formula where r is the length from the center of a pentagon to a vertex. Round up two digits after the decimal point. Here is a sample run:
Enter the length from the center to a vertex: 5.5
The area of the pentagon is 71.92
, where s is the length of a side. The side can be computed using the formula where r is the length from the center of a pentagon to a vertex. Round up two digits after the decimal point. Here is a sample run:
Enter the length from the center to a vertex: 5.5
The area of the pentagon is 71.92
import java.util.Scanner; public class ProgrammingEx4_1 { 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 * Math.pow(s, 2) / (4 * Math.tan(Math.PI / 5)); area = Math.round(area * 100) / 100.0; System.out.println("The area of the pentagon is " + area); } }
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