Area of square Circumscribed by Circle
Last Updated :
20 Feb, 2023
Given the radius(r) of circle then find the area of square which is Circumscribed by circle.
Examples:
Input : r = 3
Output :Area of square = 18
Input :r = 6
Output :Area of square = 72
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 circumscribed square is:
2 * r2
where, r is the radius of the circle in which a square is circumscribed by circle.
How does this formula work?
Assume diagonal of square is d and length of side is a.
We know from the Pythagoras Theorem, the diagonal of a
square is ?(2) times the length of a side.
i.e d2 = a2 + a2
d = 2 * a2
d = ?(2) * a
Now,
a = d / ?2
and We know diagonal of square that are Circumscribed by
Circle is equal to Diameter of circle.
so Area of square = a * a
= d / ?(2) * d / ?(2)
= d2/ 2
= ( 2 * r )2/ 2 ( We know d = 2 * r )
= 2 * r2
CPP
#include <iostream>
using namespace std;
int find_Area( int r)
{
return (2 * r * r);
}
int main()
{
int r = 3;
cout << " Area of square = "
<< find_Area(r);
return 0;
}
|
Java
class GFG {
static int find_Area( int r)
{
return ( 2 * r * r);
}
public static void main(String[] args)
{
int r = 3 ;
System.out.print( " Area of square = "
+ find_Area(r));
}
}
|
Python3
def find_Area(r):
return ( 2 * r * r)
r = 3
print ( " Area of square = " , find_Area(r))
|
C#
using System;
class GFG {
static int find_Area( int r)
{
return (2 * r * r);
}
public static void Main()
{
int r = 3;
Console.WriteLine( " Area of square = "
+ find_Area(r));
}
}
|
PHP
<?php
function find_Area( $r )
{
return (2 * $r * $r );
}
$r = 3;
echo ( "Area of square = " );
echo (find_Area( $r ));
?>
|
Javascript
<script>
function find_Area(r)
{
return (2 * r * r);
}
let r = 3;
document.write( " Area of square = "
+ find_Area(r));
</script>
|
Output:
Area of square = 18
Time Complexity: O(1)
Auxiliary Space: O(1)
Please suggest if someone has a better solution which is more efficient in terms of space and time.
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