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# 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 πa^{2}/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)a^{2}/4

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

According to formula,

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

Area of circle = πr^{2} = πa^{2}/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

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