Chapter 4, Problem 4.1PE

(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 $Area=\frac{5\times s^2}{4\times \tan \left(\frac{\pi }{5}\right)}$, where s is the length of a side. The side can be computed using the formula s = 2r $\sin \frac{\pi }{5}$, 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:

Program Plan Intro

Geometry: Area of the pentagon

Program Plan:

• Import required packages.
• Declare the main class method “pentagon”.
  • In the main method.
    • Create an object “in1” for the scanner class.
    • Get length from the user.
    • Declare the required variables for area of pentagon.
    • Calculate the area of the pentagon.
    • Display the pentagon.

Program Description Answer

The below program reads length and display the area of the pentagon.

Explanation of Solution

Program:

//import the required header files

import java.util.Scanner;

//create a class "pentagon"

public class pentagon

{

//main function   

public static void main(String[] args)

{

//Create an object

Scanner in1 = new Scanner(System.in);

//Get length from user

System.out.print("Enter the length from the center to a vertex: ");

//Get the length in "double" type

double r1 = in1.nextDouble();

//Calculate "s1"

double s1 = 2 * r1 * Math.sin(Math.PI / 5);

//Calculate "a1"

double a1 = 5 * s1 * s1 / (4 * Math.tan(Math.PI / 5));

//Display "area"

System.out.println("The area of the pentagon is " +

Math.round(a1 * 100) / 100.0);

}

}

Sample Output

Enter the length from the center to a vertex: 5.5

The area of the pentagon is 71.92