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# Calculate area of pentagon with given diagonal

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 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 ddef pentagonArea(d) :     # Formula to find area    area = (d * d * (-5 + sqrt(45)) * sqrt(sqrt(20) + 5)) / 8     return round(area , 4)   # Driver codeif __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

 

## Javascript

 

Output:

16.4291`

Time Complexity: O(1)

Auxiliary Space: O(1)