内切圆内接六边形的最大三角形
原文:https://www . geeksforgeeks . org/big-reuleaux-三角形-内切圆-内切圆-内切圆-内切圆/
给定一个边长为的正六边形，一个画出一个正方形，正方形又画出一个三角形。任务是找到这个 reuleaux 三角形的最大可能面积。 例:
Input: a = 5
Output: 28.3287
Input: a = 9
Output: 91.7848
接近:内切圆的边是 x = 1.268a 。请参考六边形内接的最大正方形。 同样，在 reuleaux 三角形中， h = x = 1.268a 。 所以，地区的 reuleaux 三角，a = 0.70477h^2 = 0.70477(1.268a)^2。 以下是上述方法的实施:
C++
// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
#include <bits/stdc++.h>
using namespace std;
// Function to find the biggest reuleaux triangle
float Area(float a)
{
// side cannot be negative
if (a < 0)
return -1;
// height of the reuleaux triangle
float h = 1.268 * a;
// area of the reuleaux triangle
float A = 0.70477 * pow(h, 2);
return A;
}
// Driver code
int main()
{
float a = 5;
cout << Area(a) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
import java.io.*;
class GFG
{
// Function to find the biggest reuleaux triangle
static float Area(float a)
{
// side cannot be negative
if (a < 0)
return -1;
// height of the reuleaux triangle
float h =(float) 1.268 * a;
// area of the reuleaux triangle
float A = (float)(0.70477 * Math.pow(h, 2));
return A;
}
// Driver code
public static void main (String[] args)
{
float a = 5;
System.out.println( Area(a));
}
}
// This code is contributed by anuj_67
Python 3
# Python3 Program to find the biggest
# Reuleaux triangle inscribed within
# in a square which in turn is
# inscribed within a hexagon
import math
# Function to find the biggest
# reuleaux triangle
def Area(a):
# side cannot be negative
if (a < 0):
return -1
# height of the reuleaux triangle
h = 1.268 * a
# area of the reuleaux triangle
A = 0.70477 * math.pow(h, 2)
return A
# Driver code
a = 5
print(Area(a),end = "\n")
# This code is contributed
# by Akanksha Rai
C
// C# Program to find the biggest Reuleaux
// triangle inscribed within in a square
// which in turn is inscribed within a hexagon
using System;
class GFG
{
// Function to find the biggest reuleaux triangle
static float Area(float a)
{
// side cannot be negative
if (a < 0)
return -1;
// height of the reuleaux triangle
float h =(float) 1.268 * a;
// area of the reuleaux triangle
float A = (float)(0.70477 * Math.Pow(h, 2));
return A;
}
// Driver code
public static void Main ()
{
float a = 5;
Console.WriteLine(Area(a));
}
}
// This code is contributed
// by Akanksha Rai
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the biggest Reuleaux
// triangle inscribed within in a square
// which in turn is inscribed within a hexagon
// Function to find the biggest
// reuleaux triangle
function Area($a)
{
// side cannot be negative
if ($a < 0)
return -1;
// height of the reuleaux triangle
$h = 1.268 * $a;
// area of the reuleaux triangle
$A = 0.70477 * pow($h, 2);
return $A;
}
// Driver code
$a = 5;
echo round(Area($a), 4);
// This code is contributed by Ryuga
?>
java 描述语言
<script>
// Javascript Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
// Function to find the biggest reuleaux triangle
function Area(a)
{
// side cannot be negative
if (a < 0)
return -1;
// height of the reuleaux triangle
let h = 1.268 * a;
// area of the reuleaux triangle
let A = 0.70477 * Math.pow(h, 2);
return A;
}
// Driver code
let a = 5;
document.write(Area(a) + "<br>");
// This code is contributed by Mayank Tyagi
</script>
Output:
28.3287
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