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

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

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)
Area = PI*r*r = (PI*a*a)/2

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C++

 // C++ Program to find the // area of a circumscribed circle #include #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#

 // 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

PHP



Output :

Area of an circumscribed circle is : 56.55