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.
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++
// 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#
// 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
<?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. ?> |
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> |
Output
Area of an circumscribed circle is : 56.55
Time Complexity: O(1)
Auxiliary Space: O(1)
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