Given here is a regular decagon, inscribed within a circle of radius r, the task is to find the area of the decagon.
Examples:
Input: r = 5
Output: 160.144
Input: r = 8
Output: 409.969
Approach:
We know, side of the decagon within the circle, a = r√(2-2cos36)(Refer here)
So, area of the decagon,
A = 5*a^2*(√5+2√5)/2 = 5 *(r√(2-2cos36))^2*(√5+2√5)/2=(5*r^2*(3-√5)*(√5+2√5))/4
Below is the implementation of the above approach:
C++
// C++ Program to find the area of the decagon // inscribed within a circle #include <bits/stdc++.h> using namespace std;
// Function to find the area of the decagon float area( float r)
{ // radius cannot be negative
if (r < 0)
return -1;
// area of the decagon
float area = (5 * pow (r, 2) * (3 - sqrt (5))
* ( sqrt (5) + (2 * sqrt (5))))
/ 4;
return area;
} // Driver code int main()
{ float r = 8;
cout << area(r) << endl;
return 0;
} |
Java
// Java Program to find the area of the decagon // inscribed within a circle import java.io.*;
class GFG {
// Function to find the area of the decagon static double area( double r)
{ // radius cannot be negative
if (r < 0 )
return - 1 ;
// area of the decagon
double area = ( 5 * Math.pow(r, 2 ) * ( 3 - Math.sqrt( 5 ))
* (Math.sqrt( 5 ) + (( 2 * Math.sqrt( 5 ))))/ 4 );
return area;
} // Driver code public static void main (String[] args) {
double r = 8 ;
System.out.println (area(r));
}
//This code is contributed by ajit } |
Python3
# Python3 Program to find the area of # the decagon inscribed within a circle from math import sqrt, pow
# Function to find the # area of the decagon def area(r):
# radius cannot be negative
if r < 0 :
return - 1
# area of the decagon
area = ( 5 * pow (r, 2 ) * ( 3 - sqrt( 5 )) *
(sqrt( 5 ) + ( 2 * sqrt( 5 )))) / 4
return area
# Driver code if __name__ = = '__main__' :
r = 8
print (area(r))
# This code is contributed # by Surendra_Gangwar |
C#
// C# Program to find the area of the // decagon inscribed within a circle using System;
class GFG
{ // Function to find the area // of the decagon static double area( double r)
{ // radius cannot be negative
if (r < 0)
return -1;
// area of the decagon
double area = (5 * Math.Pow(r, 2) *
(3 - Math.Sqrt(5)) *
(Math.Sqrt(5) +
((2 * Math.Sqrt(5))))/ 4);
return area;
} // Driver code static public void Main ()
{ double r = 8;
Console.WriteLine (area(r));
} } // This code is contributed by akt_mit |
Javascript
<script> // javascript Program to find the area of the decagon // inscribed within a circle // Function to find the area of the decagon function area( r)
{ // radius cannot be negative
if (r < 0)
return -1;
// area of the decagon
var area = (5 * Math.pow(r, 2) * (3 - Math.sqrt(5))
* (Math.sqrt(5) + ((2 * Math.sqrt(5))))/ 4);
return area;
} // Driver code var r = 8;
document.write(area(r).toFixed(3)); // This code is contributed by 29AjayKumar </script> |
PHP
<?php // PHP Program to find the area // of the decagon inscribed within // a circle // Function to find the area // of the decagon function area( $r )
{ // radius cannot be negative
if ( $r < 0)
return -1;
// area of the decagon
$area = (5 * pow( $r , 2) * (3 - sqrt(5)) *
(sqrt(5) + (2 * sqrt(5)))) / 4;
return $area ;
} // Driver code $r = 8;
echo area( $r ) . "\n" ;
// This code is contributed // by Akanksha Rai(Abby_akku) ?> |
Output
409.969
Time complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.
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