给定一个半径为r的半圆,我们必须找到可以内接在半圆上的最大正方形,底边位于直径上。
例子:
Input: r = 5
Output: 20
Input: r = 8
Output: 51.2
方法:设r为半圆的半径,a 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,由毕达哥拉斯定理:
a^2 + (a/2)^2 = r^2
5*(a^2/4) = r^2
a^2 = 4*(r^2/5) i.e. area of the square
下面是上述方法的实现:
C++
// C++ Program to find the biggest square
// which can be inscribed within the semicircle
#include
using namespace std;
// Function to find the area
// of the squaare
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
// 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 squaare
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.
Python3
# Python 3 program to find the
# biggest square which can be
# inscribed within the semicircle
# Function to find the area
# of the squaare
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 squaare
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
PHP
Javascript
输出:
20
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