# Area of decagon inscribed within the circle

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)  ` `{  ` ` `  `    ``// 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  ` `     `  `    ``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

 ` `

Output:

```409.969
```

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