Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Area of largest Circle inscribed in N-sided Regular polygon in C Program?
An n-sided regular polygon inscribed in a circle, the radius of this circle is given by the formula,
r = a/(2*tan(180/n))
Suppose a polygon have 6 faces i.e., a hexagon and as we know mathematically that the angle is 30 degree
So the radius of circle will be (a / (2*tan(30)))
Therefore, r = a√3/2
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 = Πr2 = Π * (a / (2 * tan(x))) * (a / (2*tan(x)))
Example
#include <iostream>
using namespace std;
int main() {
float area;
float n = 6; float a = 4;
float r = a / (2 * tan((180 / n) * 3.14159 / 180));
area = (3.14) * (r) * (r);
cout <<”area = ”<<area<< endl;
return 0;
}Output
area = 37.6801
Updated on: 09-Aug-2019
111 Views
Advertisements