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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 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 = 3a/2
According to formula,
Radius of circle = (√3)a22/4 / 3a/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
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