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

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  • Last Updated : 27 Aug, 2022
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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 )
  1. The formula used to calculate the perimeter of Incircle using Inradius is:
2 * \pi * r  =>  2 * \pi * (a/\sqrt3*2)

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));
   
?>

Javascript




Javascrip// JavaScript code to find the area of inscribed
// circle of equilateral triangle
let PI = 3.14159265
       
// Function to find the area of
// inscribed circle
function area_inscribed(a)
{
    return (a * a * (PI / 12))
}
   
// Function to find the perimeter of
// inscribed circle
function perm_inscribed(a)
{
    return ( PI * (a / Math.sqrt(3) ) )   
}
   
   
// Driver code
let a = 6.0
console.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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