Program to calculate area of Circumcircle of an Equilateral Triangle

Given the length of sides of an equilateral triangle. We need to write a program to find the area of Circumcircle of the given equilateral triangle.
Examples: 

Input : side = 6
Output : Area of circumscribed circle is: 37.69

Input : side = 9
Output : Area of circumscribed circle is: 84.82 

All three sides of equilateral triangle are of equal length and all three interior angles are 60 degrees.
Properties of a Circumcircle are as follows:

• The center of the circumcircle is the point where the medians of the equilateral triangle intersect.
• Circumscribed circle of an equilateral triangle is made through the three vertices of an equilateral triangle.
• The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle.

Below image shows an equilateral triangle with circumcircle: 

The formula used to calculate the area of circumscribed circle is: 

(π*a2)/3

where a is the length of the side of the given equilateral triangle.

How this formulae works?

We know that area of circle = π*r², where r is the radius of given circle.
We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3.
Therefore, area = π*r² = π*a²/3.

C++

// C++ program to find the area of Circumscribed
// circle of equilateral triangle
#include <iostream>
#include <math.h>
const double pi = 3.14159265358979323846;

using namespace std;

// function to calculate the area of circumcircle
// of equilateral triangle
float area_circumscribed(float a)
{
    return (a * a * (pi / 3));
}
// Driver code
int main()
{
    float a, Area;
    a = 6;

    // function calling
    Area = area_circumscribed(a);
    // displaying the area
    cout << "Area of CircumCircle :" << Area;
    return 0;
}

C

// C program to find the area of Circumscribed
// circle of equilateral triangle
#include <stdio.h>
#define PI 3.14159265

// function to find area of
// circumscribed circle
float area_circumscribed(float a)
{
    return (a * a * (PI / 3));
}

// Driver code
int main()
{
    float a = 6;
    printf("Area of circumscribed circle is :%f",
            area_circumscribed(a));
    return 0;
}

Java

// Java code to find the area of circumscribed
// circle of equilateral triangle
import java.lang.*;

class GFG {

    static double PI = 3.14159265;

    // function to find the area of
    // circumscribed circle
    public static double area_circumscribed(double a)
    {
        return (a * a * (PI / 3));
    }

    // Driver code
    public static void main(String[] args)
    {
        double a = 6.0;
        System.out.println("Area of circumscribed circle is :"
                            + area_circumscribed(a));
    }
}

Python3

# Python3 code to find the area of circumscribed
# circle of equilateral triangle
PI = 3.14159265

# Function to find the area of
# circumscribed circle
def area_circumscribed(a):
    return (a * a * (PI / 3))

# Driver code
a = 6.0
print("Area of circumscribed circle is :%f"
                        %area_circumscribed(a))

# This code is contributed by Anant Agarwal.

C#

// C# code to find the area of
// circumscribed circle
// of equilateral triangle
using System;

class GFG {
    static double PI = 3.14159265;

    // function to find the area of
    // circumscribed circle
    public static double area_circumscribed(double a)
    {
        return (a * a * (PI / 3));
    }

    // Driver code
    public static void Main()
    {
        double a = 6.0;
        Console.Write("Area of circumscribed circle is :" +
                       area_circumscribed(a));
    }
}

// This code is contributed by nitin mittal.

PHP

<?php
// PHP program to find the
// area of Circumscribed
// circle of equilateral triangle
$PI = 3.14159265;

// function to find area of
// circumscribed circle
function area_circumscribed($a)
{
    global $PI;
    return ($a * $a * ($PI / 3));
}

// Driver code
$a = 6;
echo("Area of circumscribed circle is :");
echo(area_circumscribed($a));

// This code is contributed by Ajit.
?>

Javascript

<script>

// javascript program to find the area of Circumscribed
// circle of equilateral triangle

let pi = 3.14159265358979323846;


// function to calculate the area of circumcircle
// of equilateral triangle
function area_circumscribed( a)
{
    return (a * a * (pi / 3));
}
// Driver code

    let a, Area;
    a = 6;

    // function calling
    Area = area_circumscribed(a);
    // displaying the area
   document.write("Area of CircumCircle :" + Area.toFixed(7));

// This code is contributed by todaysgaurav

</script>

Output:

Area of circumscribed circle is :37.6991118

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