Given the length of sides of an equilateral triangle, the task is to find the area and perimeter of Incircle of the given equilateral triangle. Examples:
Input: side = 6 Output: Area = 9.4. Perimeter = 10.88 Input: side = 9 Output: Area = 21.21, Perimeter = 16.32
Properties of an Incircle are:
- The center of the Incircle is same as the center of the triangle i.e. the point where the medians of the equilateral triangle intersect.
- Inscribed circle of an equilateral triangle is made through the midpoint of the edges of an equilateral triangle.
- The Inradius of an Incircle of an equilateral triangle can be calculated using the formula:
,
,- where
is the length of the side of equilateral triangle. - Below image shows an equilateral triangle with incircle:
is the length of the side of equilateral triangle.- Approach: Area of circle =
and perimeter of circle = 
, where r is the radius of given circle. Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3. Therefore,
- The formula used to calculate the area of Incircle using Inradius is:
and perimeter of circle = 
, where r is the radius of given circle. Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3. Therefore,
- The formula used to calculate the perimeter of Incircle using Inradius is:
C
// C program to find the area of Inscribed circle // of equilateral triangle#include <math.h>#include <stdio.h>#define PI 3.14159265 // function to find area of inscribed circlefloat area_inscribed(float a){ return (a * a * (PI / 12));} // function to find Perimeter of inscribed circlefloat perm_inscribed(float a){ return (PI * (a / sqrt(3)));} // Driver codeint main(){ float a = 6; printf("Area of inscribed circle is :%f\n", area_inscribed(a)); printf("Perimeter of inscribed circle is :%f", perm_inscribed(a)); return 0;} |
Java
// Java code to find the area of inscribed// circle of equilateral triangleimport java.lang.*; class GFG { static double PI = 3.14159265; // function to find the area of // inscribed circle public static double area_inscribed(double a) { return (a * a * (PI / 12)); } // function to find the perimeter of // inscribed circle public static double perm_inscribed(double a) { return (PI * (a / Math.sqrt(3))); } // Driver code public static void main(String[] args) { double a = 6.0; System.out.println("Area of inscribed circle is :" + area_inscribed(a)); System.out.println("\nPerimeter of inscribed circle is :" + perm_inscribed(a)); }} |
Python3
# Python3 code to find the area of inscribed # circle of equilateral triangleimport mathPI = 3.14159265 # Function to find the area of # inscribed circledef area_inscribed(a): return (a * a * (PI / 12)) # Function to find the perimeter of # inscribed circledef perm_inscribed(a): return ( PI * (a / math.sqrt(3) ) ) # Driver codea = 6.0print("Area of inscribed circle is :% f" % area_inscribed(a))print("\nPerimeter of inscribed circle is :% f" % perm_inscribed(a)) |
C#
// C# code to find the area of// inscribed circle// of equilateral triangleusing System; class GFG { static double PI = 3.14159265; // function to find the area of // inscribed circle public static double area_inscribed(double a) { return (a * a * (PI / 12)); } // function to find the perimeter of // inscribed circle public static double perm_inscribed(double a) { return (PI * (a / Math.Sqrt(3))); } // Driver code public static void Main() { double a = 6.0; Console.Write("Area of inscribed circle is :" + area_inscribed(a)); Console.Write("\nPerimeter of inscribed circle is :" + perm_inscribed(a)); }} |
PHP
<?php// PHP program to find the // area of inscribed // circle of equilateral triangle$PI = 3.14159265; // function to find area of // inscribed circlefunction area_inscribed($a){ global $PI; return ($a * $a * ($PI / 12));} // function to find perimeter of // inscribed circlefunction perm_inscribed($a){ global $PI; return ( $PI * ( $a / sqrt(3) ) );} // Driver code$a = 6;echo("Area of inscribed circle is :");echo(area_inscribed($a));echo("Perimeter of inscribed circle is :");echo(perm_inscribed($a)); ?> |
Javascript
Javascrip// JavaScript code to find the area of inscribed // circle of equilateral trianglelet PI = 3.14159265 // Function to find the area of // inscribed circlefunction area_inscribed(a){ return (a * a * (PI / 12))} // Function to find the perimeter of // inscribed circlefunction perm_inscribed(a){ return ( PI * (a / Math.sqrt(3) ) ) } // Driver codelet a = 6.0console.log("Area of inscribed circle is :", area_inscribed(a))console.log("\nPerimeter of inscribed circle is :", perm_inscribed(a))// This code is contributed by phasing17. |
Time Complexity: O(1)
Auxiliary Space: O(1)
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