Posted on by Kalkicode
Code Geometric

Find the Area of Pentagon

The problem involves calculating the area of a regular pentagon, a five-sided polygon where all sides and angles are equal. The area of a pentagon can be determined using a formula that takes the length of a side as input. Calculating the area of a pentagon is a geometric calculation used in mathematics, architecture, and engineering.

Problem Statement

Given the length of a side of a regular pentagon, we need to calculate and output the area of the pentagon. The side length is provided as input, and we are required to use the formula for the area of a pentagon to find the area.

Example

Consider a regular pentagon with a side length of 6 units. This pentagon can be visualized as follows:


        /\
       /  \
      /    \
     /      \
    /________\
        6.0

Idea to Solve

To solve this problem, we can follow these steps:

  1. Calculate the area of the pentagon using the formula: ¼ * √5 * (5 + 2 * √5) * side².
  2. Use the provided value for the side length to compute the area.

Pseudocode

function pentagon_area(side):
    area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * side * side
    return area

for each test case:
    side = pentagon side length
    result = pentagon_area(side)
    print("Pentagon [ Side :", side, "]")
    print("Area :", result)

Algorithm Explanation

  1. For each test case, calculate the area of the pentagon using the provided formula.
  2. Print the pentagon's side length and the calculated area.

Code Solution

//C Program
//Find the Area of Pentagon
#include <stdio.h>

#include <math.h>
 //Calculate area of pentagon by given side
void pentagon_area(double side)
{
	//Calculate Formula
	//¼√5(5+2√5)side²
	double area = ((double) 1 / 4) * (sqrt(5 * (5 + 2 * (sqrt(5)))) * (side * side));
	//Display the result of pentagon area
	printf(" Pentagon  [ Side : %lf ] ", side);
	printf("\n Area : %lf\n\n", area);
}
int main()
{
	//Test Cases  
	pentagon_area(6);
	pentagon_area(4);
	pentagon_area(3.5);
	return 0;
}

Output

 Pentagon  [ Side : 6.000000 ]
 Area : 61.937186

 Pentagon  [ Side : 4.000000 ]
 Area : 27.527638

 Pentagon  [ Side : 3.500000 ]
 Area : 21.075848

// Java Program
// Find the area of Pentagon
class PentagonArea
{
	//Calculate area of pentagon by given side
	public void pentagon_area(double side)
	{
		//Calculate Formula
		//¼√5(5+2√5)side²
		double area = ((double) 1 / 4) * (Math.sqrt(5 * (5 + 2 * (Math.sqrt(5)))) * (side * side));
		//Display the result of pentagon area
		System.out.print(" Pentagon [ Side : " + side + " ] ");
		System.out.print("\n Area : " + area + "\n\n");
	}
	public static void main(String[] args)
	{
		PentagonArea obj = new PentagonArea();
		//Test Cases  
		obj.pentagon_area(6);
		obj.pentagon_area(4);
		obj.pentagon_area(3.5);
	}
}

Output

 Pentagon [ Side : 6.0 ]
 Area : 61.93718642120281

 Pentagon [ Side : 4.0 ]
 Area : 27.52763840942347

 Pentagon [ Side : 3.5 ]
 Area : 21.075848157214846

// C++ Program
// Find the area of Pentagon
#include<iostream>
#include <math.h>
using namespace std;
class PentagonArea
{
	public:
		//Calculate area of pentagon by given side
		void pentagon_area(double side)
		{
			//Calculate Formula
			//¼√5(5+2√5)side²
			double area = ((double) 1 / 4) *(sqrt(5 *(5 + 2 *(sqrt(5)))) *(side *side));
			cout << " Pentagon [ Side : " << side << " ] ";
			cout << "\n Area : " << area << "\n\n";
		}
};
int main()
{
	PentagonArea obj = PentagonArea();
	//Test Cases  
	obj.pentagon_area(6);
	obj.pentagon_area(4);
	obj.pentagon_area(3.5);
	return 0;
}

Output

 Pentagon [ Side : 6 ]
 Area : 61.9372

 Pentagon [ Side : 4 ]
 Area : 27.5276

 Pentagon [ Side : 3.5 ]
 Area : 21.0758

// C# Program
// Find the area of Pentagon
using System;
class PentagonArea
{
	//Calculate area of pentagon by given side
	public void pentagon_area(double side)
	{
		//Calculate Formula
		//¼√5(5+2√5)side²
		double area = ((double) 1 / 4) * (Math.Sqrt(5 * (5 + 2 * (Math.Sqrt(5)))) * (side * side));
		Console.Write(" Pentagon [ Side : " + side + " ] ");
		Console.Write("\n Area : " + area + "\n\n");
	}
	public static void Main(String[] args)
	{
		PentagonArea obj = new PentagonArea();
		//Test Cases  
		obj.pentagon_area(6);
		obj.pentagon_area(4);
		obj.pentagon_area(3.5);
	}
}

Output

 Pentagon [ Side : 6 ]
 Area : 61.9371864212028

 Pentagon [ Side : 4 ]
 Area : 27.5276384094235

 Pentagon [ Side : 3.5 ]
 Area : 21.0758481572148

<?php
// Php Program
// Find the area of Pentagon
class PentagonArea
{
	//Calculate area of pentagon by given side
	public 	function pentagon_area($side)
	{
		//Calculate Formula
		//¼√5(5+2√5)side²
		$area = (1 / 4) *(sqrt(5 *(5 + 2 *(sqrt(5)))) *($side *$side));
		//Display the result of pentagon area
		echo(" Pentagon [ Side : ". $side ." ] ");
		echo("\n Area : ". $area ."\n\n");
	}
}

function main()
{
	$obj = new PentagonArea();
	//Test Cases  
	$obj->pentagon_area(6);
	$obj->pentagon_area(4);
	$obj->pentagon_area(3.5);
}
main();

Output

 Pentagon [ Side : 6 ]
 Area : 61.937186421203

 Pentagon [ Side : 4 ]
 Area : 27.527638409423

 Pentagon [ Side : 3.5 ]
 Area : 21.075848157215

// Node Js Program
// Find the area of Pentagon
class PentagonArea
{
	//Calculate area of pentagon by given side
	pentagon_area(side)
	{
		//Calculate Formula
		//¼√5(5+2√5)side²
		var area = (1 / 4) *(Math.sqrt(5 *(5 + 2 *(Math.sqrt(5)))) *(side *side));
		//Display the result of pentagon area
		process.stdout.write(" Pentagon [ Side : " + side + " ] ");
		process.stdout.write("\n Area : " + area + "\n\n");
	}
}

function main(args)
{
	var obj = new PentagonArea();
	//Test Cases  
	obj.pentagon_area(6);
	obj.pentagon_area(4);
	obj.pentagon_area(3.5);
}
main();

Output

 Pentagon [ Side : 6 ]
 Area : 61.93718642120281

 Pentagon [ Side : 4 ]
 Area : 27.52763840942347

 Pentagon [ Side : 3.5 ]
 Area : 21.075848157214846

#  Python 3 Program
#  Find the area of Pentagon
import math
class PentagonArea :
	# Calculate area of pentagon by given side
	def pentagon_area(self, side) :
		# Calculate Formula
		# ¼√5(5+2√5)side²
		area = (1 / 4) * (math.sqrt(5 * (5 + 2 * (math.sqrt(5)))) * (side * side))
		# Display the result of pentagon area
		print(" Pentagon [ Side : ", side ," ] ", end = "")
		print("\n Area : ", area ,"\n\n", end = "")
	

def main() :
	obj = PentagonArea()
	# Test Cases  
	obj.pentagon_area(6)
	obj.pentagon_area(4)
	obj.pentagon_area(3.5)


if __name__ == "__main__": main()

Output

 Pentagon [ Side :  6  ]
 Area :  61.93718642120281

 Pentagon [ Side :  4  ]
 Area :  27.52763840942347

 Pentagon [ Side :  3.5  ]
 Area :  21.075848157214846

#  Ruby Program
#  Find the area of Pentagon
class PentagonArea

	# Calculate area of pentagon by given side
	def pentagon_area(side)
	
		# Calculate Formula
		# ¼√5(5+2√5)side²
		# 1/4 = 0.25
		area = (0.25) * (Math.sqrt(5 * (5 + 2 * (Math.sqrt(5)))) * (side * side))
		# Display the result of pentagon area
		print(" Pentagon [ Side  : ", side ," ] ")
		print("\n Area  : ", area ,"\n\n")
	end
end
def main()

	obj = PentagonArea.new()
	# Test Cases  
	obj.pentagon_area(6)
	obj.pentagon_area(4)
	obj.pentagon_area(3.5)
end
main()

Output

 Pentagon [ Side  : 6 ] 
 Area  : 61.93718642120281

 Pentagon [ Side  : 4 ] 
 Area  : 27.52763840942347

 Pentagon [ Side  : 3.5 ] 
 Area  : 21.075848157214846


// Scala Program
// Find the area of Pentagon
class PentagonArea
{
	//Calculate area of pentagon by given side
	def pentagon_area(side: Double): Unit = {
		//Calculate Formula
		//¼√5(5+2√5)side²
		//1/4 = 0.25
		var area: Double = (0.25) * (Math.sqrt(5 * (5 + 2 * (Math.sqrt(5)))) * (side * side));
		//Display the result of pentagon area
		print(" Pentagon [ Side : " + side + " ] ");
		print("\n Area : " + area + "\n\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: PentagonArea = new PentagonArea();
		//Test Cases  
		obj.pentagon_area(6);
		obj.pentagon_area(4);
		obj.pentagon_area(3.5);
	}
}

Output

 Pentagon [ Side : 6.0 ]
 Area : 61.93718642120281

 Pentagon [ Side : 4.0 ]
 Area : 27.52763840942347

 Pentagon [ Side : 3.5 ]
 Area : 21.075848157214846

// Swift Program
// Find the area of Pentagon
import Foundation
class PentagonArea
{
	//Calculate area of pentagon by given side
	func pentagon_area(_ side: Double)
	{
		//Calculate Formula
		//¼√5(5+2√5)side²
		//1/4 = 0.25
		let area: Double = (0.25) * (sqrt(5 * (5 + 2 * (sqrt(5)))) * (side * side));
		//Display the result of pentagon area
		print(" Pentagon [ Side : ", side ," ] ");
		print(" Area : ", area ,"\n");
	}
}
func main()
{
	let obj: PentagonArea = PentagonArea();
	//Test Cases  
	obj.pentagon_area(6);
	obj.pentagon_area(4);
	obj.pentagon_area(3.5);
}
main();

Output

 Pentagon [ Side :  6.0  ]
 Area :  61.9371864212028

 Pentagon [ Side :  4.0  ]
 Area :  27.5276384094235

 Pentagon [ Side :  3.5  ]
 Area :  21.0758481572148

Output Explanation

The provided code runs three test cases and calculates the areas of regular pentagons with different side lengths. The output includes the pentagon's side length and the corresponding calculated areas.

Time Complexity

The time complexity of this code is O(1) for each test case. The calculations involve basic arithmetic operations and square root computations, which take constant time. Therefore, the overall time complexity remains constant for each test case.

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