Diagonal of a Regular Decagon

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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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 decagon
float decdiagonal(float a)
{
  
    // Side cannot be negative
    if (a < 0)
        return -1;
  
    // Length of the diagonal
    float d = 1.902 * a;
    return d;
}
  
// Driver code
int main()
{
    float a = 9;
    cout << decdiagonal(a) << endl;
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find the diagonal of a regular decdiagonal
import 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)); 
    

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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
  
# Driver code 
if __name__ == "__main__" :
  
    a = 9
    print(decdiagonal(a)) 
      
# This code is contributed by Ryuga

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find the diagonal of a regular decdiagonal
using 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..

chevron_right


PHP

Output:

17.118


My Personal Notes arrow_drop_up

Budding Web DeveloperKeen learnerAverage CoderDancer&Social Activist

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.