给定一个边长为a的n边规则多边形，任务是找到对角线的长度。
例子：
Input: a = 9, n = 10
Output: 17.119
Input: a = 4, n = 5
Output: 6.47213
方法：
We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the no. of sides in the polygon.
So, each interior angle = (n – 2) * 180/n
Now, we have to find BC = 2 * x. If we draw a perpendicular AO on BC, we will see that the perpendicular bisects BC in BO and OC, as triangles AOB and AOC are congruent to each other.
Now, t = (n – 2) * 180/2n
So, sint = x/a
Therefore, x = asint
Hence, diagonal=2x = 2asint = 2asin((n – 2) * 180/2n)
C++
// C++ Program to find the diagonal
// of a regular polygon with given side length
#include
using namespace std;
// Function to find the diagonal
// of a regular polygon
float polydiagonal(float n, float a)
{
// Side and side length cannot be negative
if (a < 0 && n < 0)
return -1;
// diagonal
// degree converted to radians
return 2 * a * sin((((n - 2) * 180) / (2 * n)) * 3.14159 / 180);
}
// Driver code
int main()
{
float a = 9, n = 10;
cout << polydiagonal(n, a) << endl;
return 0;
} Java
// Java Program to find the diagonal
// of a regular polygon with given side length
class GFG {
// Function to find the diagonal
// of a regular polygon
static float polydiagonal(float n, float a) {
// Side and side length cannot be negative
if (a < 0 && n < 0) {
return -1;
}
// diagonal
// degree converted to radians
return (float) (2 * a * Math.sin((((n - 2) * 180) / (2 * n)) * 3.14159 / 180));
}
// Driver code
public static void main(String[] args) {
float a = 9, n = 10;
System.out.printf("%.3f",polydiagonal(n, a));
}
}
// This code is contributed by 29AjayKumarPython3
# Python3 Program to find the diagonal
# of a regular polygon with given side length
import math as mt
# Function to find the diagonal
# of a regular polygon
def polydiagonal(n, a):
# Side and side length cannot
# be negative
if (a < 0 and n < 0):
return -1
# diagonal degree converted to radians
return (2 * a * mt.sin((((n - 2) * 180) /
(2 * n)) * 3.14159 / 180))
# Driver code
a, n = 9, 10
print(polydiagonal(n, a))
# This code is contributed
# by Mohit kumar 29C#
// C# Program to find the diagonal
// of a regular polygon with given side length
using System;
public class GFG{
// Function to find the diagonal
// of a regular polygon
static float polydiagonal(float n, float a) {
// Side and side length cannot be negative
if (a < 0 && n < 0) {
return -1;
}
// diagonal
// degree converted to radians
return (float) (2 * a * Math.Sin((((n - 2) * 180) / (2 * n)) * 3.14159 / 180));
}
// Driver code
static public void Main (){
float a = 9, n = 10;
Console.WriteLine(polydiagonal(n, a));
}
}
// This code is contributed by @Sachin...PHP
Javascript
输出：
17.119