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\times r^2.
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++

// 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;
}

Java

// 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.

Python3

# 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

// 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

JavaScript

<script>

// Javascript Program to find the 
// area of a circumscribed circle 
function areacircumscribed(a) 
{ 
    return (a * a * (3.1415 / 2)); 
} 

// Driver code 
    let a = 6; 
    document.write(" Area of an circumscribed circle is : ", 
        areacircumscribed(a)); 

// This code is contributed by Mayank Tyagi
</script>

PHP

<?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.
?>

Output

 Area of an circumscribed circle is : 56.55

Time Complexity: O(1)
Auxiliary Space: O(1)

Area of a Circumscribed Circle of a Square

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