Area of circle which is inscribed in equilateral triangle

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<bits/stdc++.h>
# 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

<?php
// PHP program to find the area
// of circle which is inscribed
// in equilateral triangle

// Function return the area of circle
// inscribed in equilateral triangle
function circle_inscribed($a)
{
    return 3.14 * ($a * $a) / 12;
}

// Driver code
$a = 4;

echo circle_inscribed($a);

// This code is contributed
// by Akanksha Rai(Abby_akku)

Javascript

<script>

// javascript program to find the area
// of circle which is inscribed
// in equilateral triangle

let PI = 3.14;

// Function return the area of circle
// inscribed in equilateral triangle
function circle_inscribed( a)
{
    return PI * (a * a) / 12;
}

// Driver code
let a = 4;
    document.write(circle_inscribed(a).toFixed(5));

// This code contributed by gauravrajput1

</script>

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.