Given an integer a which is the side of a regular pentagon, the task is to find and print the length of its diagonal.
Examples:
Input: a = 6
Output: 7.32
Input: a = 9
Output: 10.98
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 pentagon = 3 * 180 = 540 and each interior angle will be 108.
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(54) = x / a i.e. x = 0.61 * a
Therefore, diagonal length will be 2 * x i.e. 1.22 * a.
Below is the implementation of the above approach:
C++
// C++ Program to find the diagonal// of a regular pentagon#include <bits/stdc++.h>using namespace std;// Function to find the diagonal // of a regular pentagonfloat pentdiagonal(float a){ // Side cannot be negative if (a < 0) return -1; // Length of the diagonal float d = 1.22 * a; return d;}// Driver codeint main(){ float a = 6; cout << pentdiagonal(a) << endl; return 0;} |
Java
// Java Program to find the diagonal// of a regular pentagonclass GFG{ // Function to find the diagonal // of a regular pentagonstatic double pentdiagonal(double a){ // Side cannot be negative if (a < 0) return -1; // Length of the diagonal double d = 1.22 * a; return d;}// Driver codestatic public void main (String args[]){ double a = 6; System.out.println(pentdiagonal(a));}}// This code is contributed// by Akanksha Rai |
Python3
# Python3 Program to find the diagonal # of a regular pentagon # Function to find the diagonal # of a regular pentagon def pentdiagonal(a) : # Side cannot be negative if (a < 0) : return -1 # Length of the diagonal d = 1.22 * a return d# Driver code if __name__ == "__main__" : a = 6 print(pentdiagonal(a)) # This code is contributed by Ryuga |
C#
// C# Program to find the diagonal// of a regular pentagonusing System;public class GFG{ // Function to find the diagonal // of a regular pentagonstatic double pentdiagonal(double a){ // Side cannot be negative if (a < 0) return -1; // Length of the diagonal double d = 1.22 * a; return d;}// Driver code static public void Main (){ double a = 6; Console.WriteLine(pentdiagonal(a)); }} |
PHP
<?php// PHP Program to find the diagonal// of a regular pentagon// Function to find the diagonal // of a regular pentagonfunction pentdiagonal($a){ // Side cannot be negative if ($a < 0) return -1; // Length of the diagonal $d = 1.22 * $a; return $d;}// Driver code$a = 6;echo pentdiagonal($a);// This code is contributed // by Sach_Code?> |
Javascript
<script> // Javascript Program to find the diagonal // of a regular pentagon // Function to find the diagonal // of a regular pentagon function pentdiagonal(a) { // Side cannot be negative if (a < 0) return -1; // Length of the diagonal let d = 1.22 * a; return d; } let a = 6; document.write(pentdiagonal(a)); </script> |
7.32
Time Complexity: O(1)
Auxiliary Space: O(1)
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