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:
(?*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 = ?*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 = ?*r2 = ?*a2/3.
// 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 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 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 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# 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 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. ?> |
<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> |
Area of circumscribed circle is :37.6991118
Time Complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.