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Area of circle which is inscribed in equilateral triangle

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  • Last Updated : 27 Aug, 2022
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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.


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