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Calculate area of pentagon with given diagonal
  • Last Updated : 17 Mar, 2021

Given an integer d which is the length of the diagonal of a pentagon, the task is to find the area of that pentagon. 
 

pentagon

Examples: 
 

Input: d = 5 
Output: 16.4291
Input: d = 10 
Output: 65.7164 
 

 



Approach: Pentagon is a regular polygon having five equal sides and all equal angles. The interior angles of pentagon are of 108 degrees each and the sum of all angles of a pentagon is 540 degrees. If d is the diagonal of the pentagon then it’s area is given by: 

    $$ \frac{1}{8} {d^2 (-5+ \sqrt{45})\sqrt{ \sqrt{20} + 5 } } $$

Below is the implementation of the above approach: 
 

C++




// C++ program to find the area of
// Pentagon with given diagonal
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the area of the
// pentagon with diagonal d
float pentagonArea(float d)
{
    float area;
 
    // Formula to find area
    area = (d * d * (-5 + sqrt(45)) * sqrt(sqrt(20) + 5)) / 8;
 
    return area;
}
 
// Driver code
int main()
{
    float d = 5;
    cout << pentagonArea(d);
    return 0;
}

Java




// Java program to find the area of
// Pentagon with given diagonal
import java.text.*;
class GFG{
// Function to return the area of the
// pentagon with diagonal d
static double pentagonArea(double d)
{
    double area;
 
    // Formula to find area
    area = (d * d * (-5 + Math.sqrt(45)) * Math.sqrt(Math.sqrt(20) + 5)) / 8;
 
    return area;
}
 
// Driver code
public static void main(String[] args)
{
    double d = 5;
    DecimalFormat dec = new DecimalFormat("#0.0000");
    System.out.println(dec.format(pentagonArea(d)));
}
}
// This code is contributed by mits

Python3




# Python3 program to find the area of
# Pentagon with given diagonal
 
# from math lib import sqrt() method
from math import sqrt
 
# Function to return the area of the
# pentagon with diagonal d
def pentagonArea(d) :
 
    # Formula to find area
    area = (d * d * (-5 + sqrt(45)) * sqrt(sqrt(20) + 5)) / 8
 
    return round(area , 4)
  
 
# Driver code
if __name__ == "__main__" :
 
    d = 5
    print(pentagonArea(d))
 
# This code is contributed by Ryuga

C#




// C# program to find the area of
// Pentagon with given diagonal
using System;
 
class GFG{
// Function to return the area of the
// pentagon with diagonal d
static double pentagonArea(double d)
{
    double area;
 
    // Formula to find area
    area = (d * d * (-5 + Math.Sqrt(45)) * Math.Sqrt(Math.Sqrt(20) + 5)) / 8;
 
    return area;
}
 
// Driver code
public static void Main()
{
    double d = 5;
    Console.WriteLine("{0:F4}",pentagonArea(d));
}
}
// This code is contributed by mits

PHP




<?php
// PHP program to find the area of
// Pentagon with given diagonal
// Function to return the area of the
// pentagon with diagonal d
 Function pentagonArea($d)
{
    $area;
 
    // Formula to find area
    $area= ($d * $d * (-5 +sqrt(45)) * sqrt(sqrt(20) + 5)) / 8;
 
    return $area;
}
 
// Driver code
{
    $d = 5;
    echo(pentagonArea($d));
    return 0;
}
//This code is contributed by Mukul singh.

Javascript




<script>
// javascript program to find the area of
// Pentagon with given diagonal
 
// Function to return the area of the
// pentagon with diagonal d
function pentagonArea( d)
{
    let area;
 
    // Formula to find area
    area = (d * d * (-5 + Math.sqrt(45)) * Math.sqrt(Math.sqrt(20) + 5)) / 8;
    return area;
}
 
// Driver code
    let d = 5;
    document.write(pentagonArea(d).toFixed(4));
     
// This code is contributed by gauravrajput1
</script>
Output: 
16.4291

 

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