Area of a Circumscribed Circle of a Square

Given the side of a square then find the area of a Circumscribed circle around it.

Examples:

Input : a = 6
Output : Area of a circumscribed circle is : 56.55

Input : a = 4
Output : Area of a circumscribed circle is : 25.13

All four sides of a square are of equal length and all four angles are 90 degree. The circle is circumscribed on a given square shown by a shaded region in the below diagram.
circle-square



Properties of Circumscribed circle are as follows:

  • The center of the circumcircle is the point where the two diagonals of a square meet.
  • Circumscribed circle of a square is made through the four vertices of a square.
  • The radius of a circumcircle of a square is equal to the radius of a square.

Formula used to calculate the area of inscribed circle is:
(PI * a * a)/2
where, a is the side of a square in which a circle is circumscribed.

How does this formula work?
We know area of circle = PI*r*r.

We also know radius of circle = (square diagonal)/2
Length of diagonal = ?(2*a*a)
Radius = ?(2*a*a)/2 = ?((a*a)/2)
Area = PI*r*r = (PI*a*a)/2

C++

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// C++ Program to find the
// area of a circumscribed circle
#include <stdio.h>
#define PI 3.14159265
  
float areacircumscribed(float a)
{
    return (a * a * (PI / 2));
}
  
// Driver code
int main()
{
    float a = 6;
    printf(" Area of an circumscribed circle is : %.2f ",
           areacircumscribed(a));
    return 0;
}

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Java

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// Java program to calculate
// area of a circumscribed circle-square
import java.io.*;
class Gfg {
    // Utility Function
    static float areacircumscribed(float a)
    {
        float PI = 3.14159265f;
        return (a * a * (PI / 2));
    }
  
    // Driver Function
    public static void main(String arg[])
    {
        float a = 6;
        System.out.print("Area of an circumscribed"
                         + "circle is :");
        System.out.println(areacircumscribed(a));
    }
}
  
// The code is contributed by Anant Agarwal.

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Python3

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# Python3 Program to find the
# area of a circumscribed circle
PI = 3.14159265
  
def areacircumscribed(a):
  
    return (a * a * (PI / 2)) 
  
# Driver code
a = 6
print(" Area of an circumscribed circle is :",
        round(areacircumscribed(a), 2))
          
# This code is contributed by Smitha Dinesh Semwal

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C#

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// C# Program to find the
// area of a circumscribed circle
using System;
  
class GFG {
      
    public static double PI= 3.14159265 ;
  
    static float areacircumscribed(float a)
    {
        return (a * a * (float)(PI / 2));
    }
      
    // Driver code
    public static void Main()
    {
        float a = 6; 
          
        Console.Write(" Area of an circumscribed"
                            + " circle is : {0}"
             Math.Round(areacircumscribed(a), 2));
    
}
  
// This code is contributed by 
// Smitha Dinesh Semwal

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PHP

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<?php
// PHP Program to find the
// area of a circumscribed 
// circle
  
$PI = 3.14159265;
  
// function returns the area
function areacircumscribed($a)
{
    global $PI;
    return ($a * $a * ($PI / 2));
}
  
    // Driver code
    $a = 6;
    echo " Area of an circumscribed circle is : ",
                         areacircumscribed($a);
  
// The code is contributed by anuj_67.
?>

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Output :

 Area of an circumscribed circle is : 56.55 


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Improved By : Smitha Dinesh Semwal, vt_m



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