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