Program to calculate area of an Circle inscribed in a Square

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

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.

Inscribed circle

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: \frac{\Pi}{4} a^{2}

    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 = \Pi r^{2}

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

    Therefore, the area of an inscribed circle in a square = \Pi r^{2}
    Now, put r = a / 2
    So, the area of an inscribed circle in a square = \frac{\Pi}{4} a^{2}

    C++

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    // C++ Program to find the area of 
    // an inscribed circle in a square.
    #include<bits/stdc++.h>
    #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;
    }

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    Java

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    // 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));
        }
    }

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    Python 3

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    # 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))

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    C#

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    // 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

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    PHP

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    <?php
    // PHP 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.
    function areaOfInscribedCircle( $a)
    {
        global $PI;
        return ($PI / 4 ) *
                $a * $a;
    }
      
    // Driver Code
    $a = 8;
      
    echo "Area of an inscribed circle: ",
               areaOfInscribedCircle($a);
              
    // This code is contributed
    // by anuj_6
    ?>

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    Output:

    Area of an inscribed circle:50.24
    


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