Given an integer d which is the length of the diagonal of a pentagon, the task is to find the area of that 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:
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 dfloat pentagonArea(float d){ float area; // Formula to find area area = (d * d * (-5 + sqrt(45)) * sqrt(sqrt(20) + 5)) / 8; return area;}// Driver codeint main(){ float d = 5; cout << pentagonArea(d); return 0;} |
Java
// Java program to find the area of // Pentagon with given diagonalimport java.text.*;class GFG{// Function to return the area of the// pentagon with diagonal dstatic 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 codepublic 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() methodfrom 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 diagonalusing System;class GFG{// Function to return the area of the// pentagon with diagonal dstatic 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 codepublic 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 dfunction 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
Time Complexity: O(1)
Auxiliary Space: O(1)
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