# Area of circle which is inscribed in equilateral triangle

• Last Updated : 27 Aug, 2022

Given here is an equilateral triangle with side length a, the task is to find the area of the circle inscribed in that equilateral triangle.
Examples:

```Input : a = 4
Output : 4.1887902047863905

Input : a = 10
Output : 26.1799387799```

Approach:

Area of equilateral triangle =
Semi perimeter of equilateral triangle = (a + a + a) / 2
Radius of inscribed circle r = Area of equilateral triangle / Semi perimeter of equilateral triangle
=
=
Area of circle = PI*(r*r) =

```*** QuickLaTeX cannot compile formula:

*** Error message:
Error: Nothing to show, formula is empty
```

Below is the implementation of above approach:

## C++

 `// C++ program to find the area``// of circle which is inscribed``// in equilateral triangle``# include``# define PI 3.14``using` `namespace` `std;` `// Function return the area of circle``// inscribed in equilateral triangle``float` `circle_inscribed(``int` `a)``{``    ``return` `PI * (a * a) / 12;``}` `// Driver code``int` `main()``{``    ``int` `a = 4;` `    ``cout << circle_inscribed(a);``    ``return` `0;``}` `// This code is contributed``// by Mahadev99`

## Java

 `// Java program to find the area``// of circle which is inscribed``// in equilateral triangle``import` `java.io.*;` `class` `GFG``{` `static` `double` `PI = ``3.14``;` `// Function return the area of circle``// inscribed in equilateral triangle``static` `double` `circle_inscribed(``int` `a)``{``    ``return` `PI * (a * a) / ``12``;``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `a = ``4``;` `    ``System.out.println(circle_inscribed(a));``}``}` `// This code is contributed by anuj_67`

## Python3

 `# Python3 program to find the area of circle``# which is inscribed in equilateral triangle` `# import math library for pi value``from` `math ``import` `pi` `# Function return the area of circle``# inscribed in equilateral triangle``def` `circle_inscribed(a):``    ``return` `pi``*``(a ``*` `a) ``/` `12` `# Driver code``a ``=` `4``print``(circle_inscribed(a))`

## C#

 `// C# program to find the area``// of circle which is inscribed``// in equilateral triangle``using` `System;` `class` `GFG``{``static` `double` `PI = 3.14;` `// Function return the area of circle``// inscribed in equilateral triangle``static` `double` `circle_inscribed(``int` `a)``{``    ``return` `PI * (a * a) / 12;``}` `// Driver code``public` `static` `void` `Main ()``{``    ``int` `a = 4;` `    ``Console.WriteLine( circle_inscribed(a));``}``}` `// This code is contributed``// by inder_verma`

## PHP

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## Javascript

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Output

`4.18667`

Time complexity: O(1), since there is no loop or recursion.

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

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