Apothem of a n-sided regular polygon

• Last Updated : 22 Jun, 2022

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 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 lengthusing System; class GFG{ // Function to find the apothem// of a regular polygonstatic 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 codepublic static void Main(){    double a = 9, n = 6;    Console.WriteLine(Math.Round(polyapothem(n, a), 4));}} // This code is contributed by Ryuga



Javascript



Output:

7.79424

Time Complexity: O(1)

Auxiliary Space: O(1)

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