可内接半圆的最大正方形
给定一个半径为 r 的半圆，我们必须找到半圆中可以内接的最大正方形，底边位于直径上。
示例:
Input: r = 5
Output: 20
Input: r = 8
Output: 51.2
逼近:让 r 为半圆& a 的半径为正方形的边长。 从图中我们可以看出，圆心也是正方形底边的中点。所以在直角三角形 AOB 中，从勾股定理可知:
a^2+(a/2)^2 = r^2 5(a^2/4)= r^2 a^2 = 4(r^2/5)即广场面积
以下是上述方法的实现:
C++
// C++ Program to find the biggest square
// which can be inscribed within the semicircle
#include <bits/stdc++.h>
using namespace std;
// Function to find the area
// of the square
float squarearea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the square
float a = 4 * (pow(r, 2) / 5);
return a;
}
// Driver code
int main()
{
float r = 5;
cout << squarearea(r) << 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 square
// which can be inscribed within the semicircle
import java.io.*;
class GFG {
// Function to find the area
// of the square
static float squarearea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the square
float a = 4 * (float)(Math.pow(r, 2) / 5);
return a;
}
// Driver code
public static void main (String[] args) {
float r = 5;
System.out.println( squarearea(r));
}
}
// This code is contributed by chandan_jnu.
Python 3
# Python 3 program to find the
# biggest square which can be
# inscribed within the semicircle
# Function to find the area
# of the square
def squarearea(r):
# the radius cannot be
# negative
if (r < 0):
return -1
# area of the square
a = 4 * (pow(r, 2) / 5)
return a
# Driver code
if __name__ == "__main__":
r = 5
print(int(squarearea(r)))
# This code is contributed
# by ChitraNayal
C
// C# Program to find the
// biggest square which can be
// inscribed within the semicircle
using System;
class GFG
{
// Function to find the
// area of the square
static float squarearea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the square
float a = 4 * (float)(Math.Pow(r, 2) / 5);
return a;
}
// Driver code
public static void Main ()
{
float r = 5;
Console.WriteLine(squarearea(r));
}
}
// 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
// biggest square which can be
// inscribed within the semicircle
// Function to find the area
// of the square
function squarearea($r)
{
// the radius cannot be negative
if ($r < 0)
return -1;
// area of the square
$a = 4 * (pow($r, 2) / 5);
return $a;
}
// Driver code
$r = 5;
echo squarearea($r);
// This code is contributed
// by Shivi_Aggarwal
?>
java 描述语言
<script>
// javascript Program to find the biggest square
// which can be inscribed within the semicircle
// Function to find the area
// of the square
function squarearea(r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the square
var a = 4 * (Math.pow(r, 2) / 5);
return a;
}
// Driver code
var r = 5;
document.write( squarearea(r));
// This code contributed by Princi Singh
</script>
Output:
20
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