# Area of decagon inscribed within the circle

• Last Updated : 07 Aug, 2022

Given here is a regular decagon, inscribed within a circle of radius r, the task is to find the area of the decagon.
Examples:

```Input: r = 5
Output: 160.144

Input: r = 8
Output: 409.969``` Approach
We know, side of the decagon within the circle, a = r√(2-2cos36)(Refer here
So, area of the decagon,

A = 5*a^2*(√5+2√5)/2 = 5 *(r√(2-2cos36))^2*(√5+2√5)/2=(5*r^2*(3-√5)*(√5+2√5))/4

Below is the implementation of the above approach:

## C++

 `// C++ Program to find the area of the decagon``// inscribed within a circle``#include ``using` `namespace` `std;` `// Function to find the area of the decagon``float` `area(``float` `r)``{` `    ``// radius cannot be negative``    ``if` `(r < 0)``        ``return` `-1;` `    ``// area of the decagon``    ``float` `area = (5 * ``pow``(r, 2) * (3 - ``sqrt``(5))``                  ``* (``sqrt``(5) + (2 * ``sqrt``(5))))``                 ``/ 4;``    ``return` `area;``}` `// Driver code``int` `main()``{``    ``float` `r = 8;``    ``cout << area(r) << endl;` `    ``return` `0;``}`

Java

``````

// Java Program to find the area of the decagon
// inscribed within a circle

import java.io.*;

class GFG {

// Function to find the area of the decagon
static double area(double  r)
{

if (r < 0)
return -1;

// area of the decagon
double  area = (5 * Math.pow(r, 2) * (3 - Math.sqrt(5))
* (Math.sqrt(5) + ((2 * Math.sqrt(5))))/ 4);
return area;
}

// Driver code

public static void main (String[] args) {
double  r = 8;
System.out.println (area(r));
}
//This code is contributed by ajit
}

``````

## Python3

 `# Python3 Program to find the area of``# the decagon inscribed within a circle``from` `math ``import` `sqrt,``pow` `# Function to find the``# area of the decagon``def` `area(r):``    ` `    ``# radius cannot be negative``    ``if` `r < ``0``:``        ``return` `-``1` `    ``# area of the decagon``    ``area ``=` `(``5` `*` `pow``(r, ``2``) ``*` `(``3` `-` `sqrt(``5``)) ``*``                 ``(sqrt(``5``) ``+` `(``2` `*` `sqrt(``5``))))``/` `4``    ``return` `area` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``r ``=` `8``    ``print``(area(r))` `# This code is contributed``# by Surendra_Gangwar`

## C#

 `// C# Program to find the area of the``// decagon inscribed within a circle``using` `System;` `class` `GFG``{``        ` `// Function to find the area``// of the decagon``static` `double` `area(``double` `r)``{` `    ``// radius cannot be negative``    ``if` `(r < 0)``        ``return` `-1;` `    ``// area of the decagon``    ``double` `area = (5 * Math.Pow(r, 2) *``                  ``(3 - Math.Sqrt(5)) *``                      ``(Math.Sqrt(5) +``                 ``((2 * Math.Sqrt(5))))/ 4);``    ``return` `area;``}` `// Driver code``static` `public` `void` `Main ()``{``    ``double` `r = 8;``    ``Console.WriteLine (area(r));``}``}` `// This code is contributed by akt_mit`

## PHP

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## Javascript

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Output:

`409.969`

Time complexity: O(1)

Auxiliary Space: O(1), since no extra space has been taken.

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