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,- The formula used to calculate the area of Incircle using Inradius is:
- The formula used to calculate the perimeter of Incircle using Inradius is:
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## 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;`

`}`

*chevron_right**filter_none*## 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));`

`}`

`}`

*chevron_right**filter_none*## 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))`

*chevron_right**filter_none*## 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));`

`}`

`}`

*chevron_right**filter_none*## 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`

`));`

`?>`

*chevron_right**filter_none***Output:**Area of inscribed circle is :9.424778 Perimeter of inscribed circle is :10.882796

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- The formula used to calculate the area of Incircle using Inradius is: