Area of a Circumscribed Circle of a Square - GeeksforGeeks

18 Mar, 2021
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.  
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++
Java
Python3
C#
PHP
Javascript
// 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 codeint main(){    float a = 6;    printf(" Area of an circumscribed circle is : %.2f ",           areacircumscribed(a));    return 0;}
// Java program to calculate// area of a circumscribed circle-squareimport 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 Program to find the# area of a circumscribed circlePI = 3.14159265 def areacircumscribed(a):     return (a * a * (PI / 2)) # Driver codea = 6print(" 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 circleusing 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
<?php// PHP Program to find the// area of a circumscribed// circle $PI = 3.14159265; // function returns the areafunction areacircumscribed($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.?>
<script> // Javascript Program to find the// area of a circumscribed circlefunction 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>
Output :  
 Area of an circumscribed circle is : 56.55 
 
Smitha Dinesh Semwal
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