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 = \frac{\sqrt{3}}{4} a^2
Semi perimeter of equilateral triangle = (a + a + a) / 2

Radius of inscribed circle r = Area of equilateral triangle / Semi perimeter of equilateral triangle
                                            = \frac{\sqrt{3}}{4} a^2  /  {\frac{3a}{2}}
                                            =  \frac{a}{2{\sqrt3}}

Area of circle = PI*(r*r) =  \frac{\pi a^{2}}{12}

Below is the implementation of above approach:

C++

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// 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 retun 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

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Java

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// 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 retun 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

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Python3

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# 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 retun 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))

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C#

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// C# program to find the area 
// of circle which is inscribed
// in equilateral triangle 
using System;
  
class GFG 
{
static double PI = 3.14;
  
// Function retun 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

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PHP

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

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Output:

4.1887902047863905


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