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 decagonfloat 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 codeint 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 circlefrom math import sqrt,pow# Function to find the # area of the decagondef 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 codeif __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 decagonfunction 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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