Area of circle which is inscribed in an equilateral triangle?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa²/12.

Lets see how this formula is derived,

Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

Area of triangle of side a = (√3)a²/4

Semi-perimeter of triangle of side a = 3^a/2

According to formula,

Radius of circle = (√3)a²2/4 / 3^a/2 = a/2√3

Area of circle = πr² = πa²/12

Example Code

#include <stdio.h>
int main(void) {
   int a = 5;
   float pie = 3.14;
   float area = (float)((pie*a*a)/12);
   printf("the area of circle inscribed in the triangle of side %d is %f",a,area);
   return 0;
}

Output

the area of circle inscribed in the triangle of side 5 is 6.541667