Calcular el área del pentágono con la diagonal dada

Dado un entero d que es la longitud de la diagonal de un pentágono , la tarea es encontrar el área de ese pentágono. 
 

Ejemplos: 
 

Entrada: d = 5 
Salida: 16,4291
Entrada: d = 10 
Salida: 65,7164 
 

Enfoque: Pentágono es un polígono regular que tiene cinco lados iguales y todos los ángulos iguales. Los ángulos interiores del pentágono son de 108 grados cada uno y la suma de todos los ángulos de un pentágono es de 540 grados. Si d es la diagonal del pentágono, entonces su área está dada por: 

A continuación se muestra la implementación del enfoque anterior: 
 

// 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 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 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# 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 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.

<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>

16.4291

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)