Java Program to find the area of a pentagon

Program

import java.util.Scanner;
public class AreaOfPentagon {
    public static void main(String args[]) {
        int apothem, side;
        float area, area_num;
        Scanner sc = new Scanner(System.in);
        System.out.println("Enter the apothem:\t");
        apothem = sc.nextInt();
        System.out.println("Enter the length of side:\t");
        side = sc.nextInt();
        area_num = (5 * side * apothem);
        area = area_num / 2;
        System.out.println("Area of pentagon: " + area);
    }
}

Purpose

This program calculates the area of a pentagon using its apothem and the length of a side. The formula for the area of a regular pentagon is:

[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} ]

1. Declare Variables

int apothem, side;
float area, area_num;

• apothem: Stores the apothem of the pentagon (distance from the center to the midpoint of a side).
• side: Stores the length of one side of the pentagon.
• area_num: Used to calculate the numerator of the area formula.
• area: Stores the final calculated area of the pentagon.

2. Take Input

Scanner sc = new Scanner(System.in);
System.out.println("Enter the apothem:\t");
apothem = sc.nextInt();
System.out.println("Enter the length of side:\t");
side = sc.nextInt();

• Step 1: Create a Scanner object to read user input.
• Step 2: Prompt the user to enter the apothem and store the input in the variable apothem.
• Step 3: Prompt the user to enter the length of a side and store it in the variable side.

3. Calculate the Area

area_num = (5 * side * apothem);
area = area_num / 2;

• Step 1: Calculate the numerator: [ \text{area_num} = 5 \times \text{side} \times \text{apothem} ]

  • Explanation: 5 * side computes the perimeter of the pentagon (5 sides of equal length).
  • Multiply the perimeter by the apothem.

• Step 2: Compute the final area: [ \text{area} = \frac{\text{area_num}}{2} ]

4. Display the Area

System.out.println("Area of pentagon: " + area);

• Outputs the calculated area to the console.

Execution Steps

1. Input: apothem = 5, side = 6.
2. Calculate:
   • Perimeter: ( 5 \times 6 = 30 )
   • Numerator: ( 30 \times 5 = 150 )
   • Area: ( \frac{150}{2} = 75.0 )
3. Output:

   Area of pentagon: 75.0
   

Output

Enter the apothem:	
7
Enter the length of side:	
10
Area of pentagon: 175.0