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

 Live Demo

#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

Karthikeya Boyini

Published on 15-Jul-2019 13:12:45

• Related Questions & Answers
• Area of circle which is inscribed in equilateral triangle in C Program?
• Area of a square inscribed in a circle which is inscribed in an equilateral triangle in C Program?
• Area of a square inscribed in a circle which is inscribed in an equilateral triangle in C Program?
• Area of a triangle inscribed in a rectangle which is inscribed in an ellipse?
• Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle?
• Area of a circle inscribed in a rectangle which is inscribed in a semicircle?
• Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle in C?
• Area of a triangle inscribed in a rectangle which is inscribed in an ellipse In C Program?
• Area of a circle inscribed in a rectangle which is inscribed in a semicircle in C?
• Count of distinct rectangles inscribed in an equilateral triangle in C++
• Program to calculate the Area and Perimeter of Incircle of an Equilateral Triangle What is Equilateral Triangle in C?
• Area of circle inscribed within rhombus?
• Program to calculate area of Circumcircle of an Equilateral Triangle
• Area of a square inscribed in a circle which is inscribed in a hexagon in C Program?
• C Program for Area of a square inscribed in a circle which is inscribed in a hexagon?