# 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 = 5Output:160.144Input:r = 8Output:409.969

**Approach**:

We know, side of the decagon within the circle, **a = râˆš(2-2cos36)**(Refer here)

So, area of the decagon,

A = 5*a^2*(âˆš5+2âˆš5)/2 = 5 *(râˆš(2-2cos36))^2*(âˆš5+2âˆš5)/2=(5*r^2*(3-âˆš5)*(âˆš5+2âˆš5))/4

Below is the implementation of the above approach:

## C++

`// C++ Program to find the area of the decagon` `// inscribed within a circle` `#include <bits/stdc++.h>` `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 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

`<?php` `// PHP Program to find the area` `// of the decagon inscribed within` `// a circle` `// Function to find the area` `// of the decagon` `function` `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` `$area` `;` `}` `// Driver code` `$r` `= 8;` `echo` `area(` `$r` `) . ` `"\n"` `;` `// This code is contributed` `// by Akanksha Rai(Abby_akku)` `?>` |

## Javascript

`<script>` `// javascript Program to find the area of the decagon` `// inscribed within a circle` ` ` `// Function to find the area of the decagon` `function` `area( r)` `{` ` ` `// radius cannot be negative` ` ` `if` `(r < 0)` ` ` `return` `-1;` ` ` `// area of the decagon` ` ` `var` `area = (5 * Math.pow(r, 2) * (3 - Math.sqrt(5))` ` ` `* (Math.sqrt(5) + ((2 * Math.sqrt(5))))/ 4);` ` ` `return` `area;` `}` `// Driver code` `var` `r = 8;` `document.write(area(r).toFixed(3));` `// This code is contributed by 29AjayKumar` `</script>` |

**Output:**

409.969

**Time complexity:** O(1)

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