Apothem of a n-sided regular polygon

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 Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 using namespace std;    // Function to find the apothem // of a regular polygon float 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 code int 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 length import 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 code public 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 # length from math import tan    # Function to find the apothem # of a regular polygon def 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 code if __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



Output:

7.79424

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