What is the area of ​​a circle inscribed in an equilateral triangle?

The area of ​​the inscribed circle of an equilateral triangle can be found using the following formula Mathematical formula πa²/12.

Let us see how this formula is derived,

The formula for the radius of an inscribed circle = the area of ​​a triangle / the half circumference of the triangle.

Area of ​​triangle side a = (√3)a²/4

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

According to the formula,

The radius of the circle = (√3)a²2/ 4 / 3^a/2 = a/2√3

Area of ​​circle = πr² = πa²/ 12

Sample code

Real-time demonstration

#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

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