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Program to calculate area of an Circle inscribed in a Square
• Last Updated : 03 Aug, 2018

Given the side of a square. The task is to find the area of an inscribed circle in a square.

Examples:

Input : a = 8
Output : Area of an inscribed circle: 50.24

Input : a = 12.04
Output : Area of an inscribed circle: 113.795


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Given a square i.e. all sides of a square are of equal length and all four angles are 90 degrees. Below diagram depicts an inscribed circle in a square. Properties of an inscribed circle in a square:

• The diameter of an inscribed circle in a square is equal to the length of the side of a square.
• With at least one measure of the circle or the square, the area and the perimeter of the square can be calculated in which the circle is inscribed.
• The center of the square and the center of the circle lie at a same point.
• when at least one measure of the circle or the square is given, the circumference and area of the circle can be calculated.
• Formula to find the area of an inscribed circle: where a is the side of a square in which a circle is inscribed.

How does the formula works?
Assume a is the side of a square and we know that a square has 4 sides.

Area of a circle = where r is the radius of a circle and area of a square = a2

Therefore, the area of an inscribed circle in a square = Now, put r = a / 2
So, the area of an inscribed circle in a square = ## C++

 // C++ Program to find the area of   // an inscribed circle in a square.  #include  #define PI 3.14  using namespace std;     // Function to find area of an   // inscribed circle in a square.  float areaOfInscribedCircle(float a)  {      return ( PI / 4 ) * a * a;  }     // Driver's code  int main()  {      float a = 8;             cout << "Area of an inscribed circle: "          << areaOfInscribedCircle(a);                  return 0;  }

## Java

 // Java Program to find the area of   // an inscribed circle in a square.  import java.io.*;     class GFG {             static double PI = 3.14;             // Function to find area of an       // inscribed circle in a square.      static double areaOfInscribedCircle(float a)      {          return ( PI / 4 ) * a * a;      }         // Driver code      public static void main (String[] args)      {          float a = 8;                 System.out.println("Area of an inscribed"         + " circle: " + areaOfInscribedCircle(a));      }  }

## Python 3

 # Python Program to find the area of   # an inscribed circle in a square.         PI = 3.14        # Function to find area of an   # inscribed circle in a square.  def areaOfInscribedCircle(a):      return ( PI / 4 ) * a * a     # Driver code  a = 8 print("Area of an inscribed circle:",    round(areaOfInscribedCircle(a), 2))

## C#

 // C# Program to find the   // area of an inscribed   // circle in a square.  using System;     class GFG   {      static double PI = 3.14;             // Function to find area        // of an inscribed circle      // in a square.      static double areaOfInscribedCircle(float a)      {          return (PI / 4 ) * a * a;      }         // Driver code      public static void Main ()      {          float a = 8;                 Console.WriteLine("Area of an inscribed" +                                        " circle: " +                          areaOfInscribedCircle(a));      }  }     // This code is contributed  // by anuj_6

## PHP

 

Output:

Area of an inscribed circle:50.24


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