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# Program to calculate the Area and Perimeter of Incircle of an Equilateral Triangle

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:

• 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,
1. The formula used to calculate the area of Incircle using Inradius is: 1. 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 #include #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

 

## 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)