Given here the side length a of a regular n-sided polygon, the task is to find the length of its Apothem.
Apothem is the line drawn from the center of the polygon that is perpendicular to one of its sides.
Examples:
Input a = 9, n = 6 Output: 7.79424 Input: a = 8, n = 7 Output: 8.30609
Approach:
In the figure, we see the polygon can be divided into n equal triangles.
Looking into one of the triangles, we see the whole angle at the centre can be divided into = 360/n
So, angle t = 180/n
now, tan t = a/2h
So, h = a/(2*tan t)
here, h is the apothem,
so, apothem = a/(2*tan(180/n))
Below is the implementation of the above approach.
C++
// C++ Program to find the apothem// of a regular polygon with given side length#include <bits/stdc++.h>using namespace std;// Function to find the apothem// of a regular polygonfloat polyapothem(float n, float a){ // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // Degree converted to radians return a / (2 * tan((180 / n) * 3.14159 / 180));}// Driver codeint main(){ float a = 9, n = 6; cout << polyapothem(n, a) << endl; return 0;} |
Java
// Java Program to find the apothem of a // regular polygon with given side lengthimport java.util.*;class GFG{ // Function to find the apothem // of a regular polygon double polyapothem(double n, double a) { // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // Degree converted to radians return (a / (2 * java.lang.Math.tan((180 / n) * 3.14159 / 180))); }// Driver codepublic static void main(String args[]){ double a = 9, n = 6; GFG g=new GFG(); System.out.println(g.polyapothem(n, a));}}//This code is contributed by Shivi_Aggarwal |
Python3
# Python 3 Program to find the apothem# of a regular polygon with given side# lengthfrom math import tan# Function to find the apothem# of a regular polygondef polyapothem(n, a): # Side and side length cannot be negative if (a < 0 and n < 0): return -1 # Degree converted to radians return a / (2 * tan((180 / n) * 3.14159 / 180))# Driver codeif __name__ == '__main__': a = 9 n = 6 print('{0:.6}'.format(polyapothem(n, a))) # This code is contributed by# Sahil_Shelangia |
C#
// C# Program to find the apothem of a // regular polygon with given side length using System;class GFG { // Function to find the apothem // of a regular polygon static double polyapothem(double n, double a) { // Side and side length cannot // be negative if (a < 0 && n < 0) return -1; // Degree converted to radians return (a / (2 * Math.Tan((180 / n) * 3.14159 / 180))); } // Driver code public static void Main() { double a = 9, n = 6; Console.WriteLine(Math.Round(polyapothem(n, a), 4)); } } // This code is contributed by Ryuga |
PHP
<?php// PHP Program to find the apothem of a// regular polygon with given side length// Function to find the apothem// of a regular polygonfunction polyapothem($n, $a){ // Side and side length cannot // be negative if ($a < 0 && $n < 0) return -1; // Degree converted to radians return $a / (2 * tan((180 / $n) * 3.14159 / 180));}// Driver code$a = 9; $n = 6;echo polyapothem($n, $a) . "\n";// This code is contributed// by Akanksha Rai?> |
Javascript
<script>// javascript Program to find the apothem of a // regular polygon with given side length// Function to find the apothem// of a regular polygonfunction polyapothem(n , a){ // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // Degree converted to radians return (a / (2 * Math.tan((180 / n) * 3.14159 / 180)));}// Driver codevar a = 9, n = 6;document.write(polyapothem(n, a).toFixed(5));// This code contributed by Princi Singh </script> |
Output:
7.79424
Time Complexity: O(1)
Auxiliary Space: O(1)
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