Given an integer a which is the side of a regular decagon, the task is to find and print the length of its diagonal.
Examples:
Input: a = 5
Output: 9.51
Input: a = 9
Output: 17.118
Approach: We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the no. of sides in the polygon.
So, sum of interior angles of decagon = 8 * 180 = 1440 and each interior angle will be 144.
Now, we have to find BC = 2 * x. If we draw a perpendicular AO on BC, we will see that the perpendicular bisects BC in BO and OC, as triangles AOB and AOC are congruent to each other.
So, in triangle AOB, sin(72) = x / a i.e. x = 0.951 * a
Therefore, diagonal length will be 2 * x i.e. 1.902 * a.
Below is the implementation of the above approach:
C++
// C++ program to find the diagonal// of a regular decagon#include <bits/stdc++.h>using namespace std;// Function to return the diagonal// of a regular decagonfloat decdiagonal(float a){ // Side cannot be negative if (a < 0) return -1; // Length of the diagonal float d = 1.902 * a; return d;}// Driver codeint main(){ float a = 9; cout << decdiagonal(a) << endl; return 0;} |
Java
// Java program to find the diagonal of a regular decdiagonalimport java.util.*; import java.lang.*; import java.io.*; public class GFG { // Function to return the diagonal of a regular decdiagonal static double decdiagonal(double a) { //side cannot be negative if(a<0) return -1; // length of the diagonal double d=1.902*a; return d; } // Driver code public static void main(String[] args) { int a = 9; System.out.println(decdiagonal(a)); } } |
Python3
# Python3 program to find the diagonal # of a regular decagon # Function to return the diagonal # of a regular decagon def decdiagonal(a) : # Side cannot be negative if (a < 0) : return -1 # Length of the diagonal d = 1.902 * a return d # Driver code if __name__ == "__main__" : a = 9 print(decdiagonal(a)) # This code is contributed by Ryuga |
C#
// C# program to find the diagonal of a regular decdiagonalusing System;public class GFG { // Function to return the diagonal of a regular decdiagonal static double decdiagonal(double a) { //side cannot be negative if(a<0) return -1; // length of the diagonal double d=1.902*a; return d; } // Driver code public static void Main() { int a = 9; Console.WriteLine(decdiagonal(a)); } } // This code is contributed by anuj_67.. |
PHP
<?php// PHP program to find the diagonal// of a regular decagon// Function to return the diagonal// of a regular decagonfunction decdiagonal($a){ // Side cannot be negative if ($a < 0) return -1; // Length of the diagonal $d = 1.902 * $a; return $d;}// Driver code$a = 9;echo decdiagonal($a);// This code is contributed by ajit.?> |
Javascript
<script>// javascript program to find the diagonal of a regular decdiagonal// Function to return the diagonal of a regular decdiagonalfunction decdiagonal(a) { // side cannot be negativeif(a < 0)return -1;// length of the diagonalvar d = 1.902*a;return d; } // Driver code var a = 9; document.write(decdiagonal(a)); // This code contributed by Princi Singh </script> |
17.118
Time Complexity: O(1)
Auxiliary Space: O(1)
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