Program to calculate area of Circumcircle of an Equilateral Triangle

A circumcircle is a circle that passes through all vertices of a polygon. For an equilateral triangle, the circumcircle can be calculated using the relationship between the triangle's side length and the circle's radius.

Syntax

Area = (? × a²) / 3
where a = side length of equilateral triangle

Mathematical Formula

The area of the circumcircle of an equilateral triangle with side length a is given by −

Area = (? × a²) / 3

This formula is derived from the fact that the circumradius R of an equilateral triangle is R = a / ?3, and the area of a circle is ? × R².

Example

The following program calculates the area of circumcircle of an equilateral triangle −

#include <stdio.h>
#include <math.h>

int main() {
    int a = 5;
    float area;
    float pi = 3.14159;
    
    printf("Program to calculate area of Circumcircle of an Equilateral Triangle<br>");
    printf("The side of the triangle is %d<br>", a);
    
    area = (pi * a * a) / 3;
    
    printf("The area of circumcircle of an equilateral triangle is %.2f<br>", area);
    return 0;
}

Output

Program to calculate area of Circumcircle of an Equilateral Triangle
The side of the triangle is 5
The area of circumcircle of an equilateral triangle is 26.18

Key Points

• The circumcircle passes through all three vertices of the equilateral triangle.
• Using a more precise value of ? (3.14159) gives better accuracy than 3.14.
• The formula directly relates the triangle's side length to the circumcircle's area.

Conclusion

The area of a circumcircle of an equilateral triangle can be efficiently calculated using the formula (? × a²) / 3. This mathematical relationship provides a direct way to find the circumcircle area given the triangle's side length.