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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 Cicumscribed  // circle of equilateral triangle #include #include 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 Cicumscribed  // circle of equilateral triangle #include #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_cicumscribed(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_cicumscribed(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_cicumscribed(a):     return (a * a * (PI / 3))        # Driver code a = 6.0 print("Area of circumscribed circle is :%f"                         %area_cicumscribed(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_cicumscribed(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_cicumscribed(a));     } }    // This code is contributed by nitin mittal.

PHP



Output:

Area of circumscribed circle is :37.6991118