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Program to calculate the Area and Perimeter of Incircle of an Equilateral Triangle
  • Last Updated : 27 Nov, 2018

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:
      a / (\sqrt3 * 2) ,
    

    where  a is the length of the side of equilateral triangle.

  • Below image shows an equilateral triangle with incircle:
    
    
  • Approach:

    Area of circle = \pi*r^2 and perimeter of circle =  2 * \pi * r , where r is the radius of given circle.

    Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3.
    Therefore,

    1. The formula used to calculate the area of Incircle using Inradius is:
       \pi r^2  =>  ( \pi * a^2 ) / (3 * 2 ) 
      
    2. The formula used to calculate the perimeter of Incircle using Inradius is:
       2 * \pi * r  =>  2 * \pi * (a/\sqrt3*2) 
      
    3. 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 circle
      float area_inscribed(float a)
      {
          return (a * a * (PI / 12));
      }
        
      // function to find Perimeter of inscribed circle
      float perm_inscribed(float a)
      {
          return (PI * (a / sqrt(3)));
      }
        
      // Driver code
      int 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 triangle
      import 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 triangle
      import math
      PI = 3.14159265
            
      # Function to find the area of 
      # inscribed circle
      def area_inscribed(a):
          return (a * a * (PI / 12))
        
      # Function to find the perimeter of 
      # inscribed circle
      def perm_inscribed(a):
          return ( PI * (a / math.sqrt(3) ) )    
        
        
      # Driver code
      a = 6.0
      print("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 triangle
      using 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 circle
      function area_inscribed($a)
      {
          global $PI;
          return ($a * $a * ($PI / 12));
      }
        
      // function to find perimeter of 
      // inscribed circle
      function 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));
        
      ?>

      
      

      Output:

      Area of inscribed circle is :9.424778
      Perimeter of inscribed circle is :10.882796
      

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