Given a regular polygon of N sides with side length a. The task is to find the area of the Circle which inscribed in the polygon.
Note : This problem is mixed version of This and This
Examples:
Input: N = 6, a = 4 Output: 37.6801 Explanation:
In this, the polygon have 6 faces and as we see in fig.1 we clearly see that the angle x is 30 degree so the radius of circle will be ( a / (2 * tan(30))) Therefore, r = a?3/2 Input: N = 8, a = 8 Output: 292.81 Explanation:
In this, the polygon have 8 faces and as we see in fig.2 we clearly see that the angle x is 22.5 degree so the radius of circle will be ( a / (2 * tan(22.5))) Therefore, r = a/0.828
Approach: In the figure above, we see the polygon can be divided into N equal triangles. Looking into one of the triangles, we see that the whole angle at the center can be divided into = 360/N
So, angle x = 180/n
Now, tan(x) = (a / 2) * r
So, r = a / ( 2 * tan(x))
So, Area of the Inscribed Circle is,
A = ?r² = ? * (a / (2 * tan(x))) * (a / (2*tan(x)))
Below is the implementation of the above approach:
C++
// C++ Program to find the area of a circle in// inscribed in polygon#include <bits/stdc++.h>using namespace std;// Function to find the area// of a circlefloat InscribedCircleArea(float n, float a){ // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // degree converted to radians float r = a / (2 * tan((180 / n) * 3.14159 / 180)); // area of circle float Area = (3.14) * (r) * (r); return Area;}// Driver codeint main(){ // no. of sides float n = 6; // side length float a = 4; cout << InscribedCircleArea(n, a) << endl; return 0;} |
Java
// Java Program to find the area of a circle// inscribed in a polygonimport java.io.*;class GFG { // Function to find the area // of a regular polygon static float InscribedCircleArea(float n, float a) { // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // degree converted to radians float r = a / (float)(2 * Math.tan((180 / n) * 3.14159 / 180)); // area of circle float Area = (float)(3.14) * (r) * (r); return Area; } // Driver code public static void main(String[] args) { // no. of sides float n = 6; // side length float a = 4; System.out.println(InscribedCircleArea(n, a)); }} |
Python3
# Python 3 Program to find the area # of a circle inscribed# in a polygonfrom math import tan# Function to find the area of a # circledef InscribedCircleArea(n, a): # Side and side length cannot # be negative if (a < 0 and n < 0): return -1 # degree converted to radians r = a/(2 * tan((180 / n) * 3.14159 / 180)); # area of circle Area = 3.14 * r * r return Area# Driver codeif __name__ == '__main__': a = 4 n = 6 print('{0:.6}'.format(InscribedCircleArea(n, a)))# This code is contributed by# Chandan Agrawal |
C#
// C# Program to find the area of a circle // inscribed in a polygon using System;class GFG { // Function to find the area // of a regular polygon static float InscribedCircleArea(float n, float a) { // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // degree converted to radians float r = a / (float)(2 * Math.Tan((180 / n) * 3.14159 / 180)); // area of circle float Area = (float)(3.14) * (r) * (r); return Area; } // Driver code public static void Main() { // no. of sides float n = 6; // side length float a = 4; Console.WriteLine(InscribedCircleArea(n, a)); }} // This code is contributed by Ryuga |
PHP
<?php // PHP Program to find the area // of a circle inscribed// in a polygon// Function to find the area of a // circlefunction InscribedCircleArea($n, $a){ // Side and side length cannot // be negative if ($a < 0 && $n < 0) return -1; // degree converted to radians $r = $a / (2 * tan((180 / $n) * 3.14159 / 180)); // area of circle $Area = 3.14 * $r * $r; return $Area;} // Driver code$a = 4;$n = 6;echo(InscribedCircleArea($n, $a));// This code contributed by PrinciRaj1992 ?> |
Javascript
<script>// Javascript Program to find the area of a circle// inscribed in a polygon // Function to find the area // of a regular polygon function InscribedCircleArea( n ,a) { // Side and side length cannot be negative if (a < 0 && n < 0) return -1; // degree converted to radians let r = a / (2 * Math.tan((180 / n) * 3.14159 / 180)); // area of circle let Area = (3.14) * (r) * (r); return Area; } // Driver code // no. of sides let n = 6; // side length let a = 4; document.write(InscribedCircleArea(n, a).toFixed(4)); // This code is contributed by 29AjayKumar </script> |
Output:
37.6801
Time Complexity: O(1)
Auxiliary Space: O(1)
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