六边形内接的最大正方形
给定一个规则的六边形长度 a ，任务是找到可以在其中内接的最大正方形的面积。 例:
输入: a = 6 输出: 57.8817 输入: a = 8 输出: 102.901
方法:我们将导出的正方形将具有六边形的相同中心和轴。这是因为如果我们旋转它，正方形会变小。
六边形的边相等，即 a = b + c 。 现在，让 d 为内接正方形边长， 然后为正方形顶边， d = 2 * c * sin(60) 。 还有，左边的方块， d = a + 2 * b * sin(30) 。 代替 c，d = 2 (a–b) sin(60)。 现在取 d 重新排列，我们得到，b/a =(2 * sin(60)–1)/(2 *(sin(30)+sin(60))) 所以，b/a = 2–√3 现在，代入正方形左手边方程中 b 和 a 的关系，我们得到， d/a = 0
以下是上述方法的实现:
C++
// C++ program to find the area of the largest square
// that can be inscribed within the hexagon
#include <bits/stdc++.h>
using namespace std;
// Function to find the area
// of the square
float squareArea(float a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Area of the square
float area = pow(1.268, 2) * pow(a, 2);
return area;
}
// Driver code
int main()
{
float a = 6;
cout << squareArea(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 area of the largest square
// that can be inscribed within the hexagon
class Solution {
// Function to find the area
// of the square
static float squareArea(float a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Area of the square
float area = (float)(Math.pow(1.268, 2) * Math.pow(a, 2));
return area;
}
// Driver code
public static void main(String args[])
{
float a = 6;
System.out.println(squareArea(a));
}
}
// This code is contributed by Arnab Kundu
Python 3
# Python program to find the area of the largest square
# that can be inscribed within the hexagon
# Function to find the area
# of the square
def squareArea(a):
# Side cannot be negative
if (a < 0):
return -1;
# Area of the square
area = (1.268 ** 2) * (a ** 2);
return area;
# Driver code
a = 6;
print(squareArea(a));
# This code contributed by PrinciRaj1992
C
// C# program to find the area of the largest square
// that can be inscribed within the hexagon
using System;
class Solution {
// Function to find the area
// of the square
static float squareArea(float a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Area of the square
float area = (float)(Math.Pow(1.268, 2) * Math.Pow(a, 2));
return area;
}
// Driver code
public static void Main()
{
float a = 6;
Console.WriteLine(squareArea(a));
}
}
// This code is contributed by anuj_67..
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find the area of the largest square
// that can be inscribed within the hexagon
// Function to find the area
// of the square
function squareArea($a)
{
// Side cannot be negative
if ($a < 0)
return -1;
// Area of the square
$area = pow(1.268, 2) * pow($a, 2);
return $area;
}
// Driver code
$a = 6;
echo squareArea($a), "\n";
// This code is contributed by Tushil
?>
java 描述语言
<script>
// javascript program to find the area of the largest square
// that can be inscribed within the hexagon
// Function to find the area
// of the square
function squareArea(a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Area of the square
var area = (Math.pow(1.268, 2) * Math.pow(a, 2));
return area;
}
// Driver code
var a = 6;
document.write(squareArea(a).toFixed(5));
// This code is contributed by Princi Singh
</script>
Output:
57.8817
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