可内接半圆的最大梯形
给定一个半径为 r 的半圆，任务是找到半圆内可内接的最大梯形，其基位于直径上。 例:
Input: r = 5
Output: 32.476
Input: r = 8
Output: 83.1384
逼近:设 r 为半圆半径， x 为梯形下缘， y 为上缘，&T8】h 为梯形高度。 现在从图中，
r^2 = h^2 + (y/2)^2 或，4r^2 = 4h^2+y^2 y^2 = 4r^2–4h 2 y = 2√(R2–H2) 我们知道，梯形的面积，A = (x + y)h/2 所以，a = HR+h√(R2–H2) 取这个面积函数相对于 h 的导数， (注意 r 是一个常数，因为我们从半径 r 的半圆开始) da/DH = r+√(r^2–h^2)–h^2/√(r^2–h^2) 为了找到临界点，我们将导数设置为零并求解 h，我们得到 h = √3/2 * r So，x = 2 * r & y = r So，a =(3 √3 * r^2)/4**t13】
以下是上述方式的实施 :
C++
// C++ Program to find the biggest trapezoid
// which can be inscribed within the semicircle
#include <bits/stdc++.h>
using namespace std;
// Function to find the area
// of the biggest trapezoid
float trapezoidarea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the trapezoid
float a = (3 * sqrt(3) * pow(r, 2)) / 4;
return a;
}
// Driver code
int main()
{
float r = 5;
cout << trapezoidarea(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 trapezoid
// which can be inscribed within the semicircle
import java.util.*;
import java.lang.*;
import java.io.*;
class GFG{
// Function to find the area
// of the biggest trapezoid
static float trapezoidarea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the trapezoid
float a = (3 * (float)Math.sqrt(3)
* (float)Math.pow(r, 2)) / 4;
return a;
}
// Driver code
public static void main(String args[])
{
float r = 5;
System.out.printf("%.3f",trapezoidarea(r));
}
}
Python 3
# Python 3 Program to find the biggest trapezoid
# which can be inscribed within the semicircle
# from math import everything
from math import *
# Function to find the area
# of the biggest trapezoid
def trapezoidarea(r) :
# the radius cannot be negative
if r < 0 :
return -1
# area of the trapezoid
a = (3 * sqrt(3) * pow(r,2)) / 4
return a
# Driver code
if __name__ == "__main__" :
r = 5
print(round(trapezoidarea(r),3))
# This code is contributed by ANKITRAI1
C
// C# Program to find the biggest
// trapezoid which can be inscribed
// within the semicircle
using System;
class GFG
{
// Function to find the area
// of the biggest trapezoid
static float trapezoidarea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the trapezoid
float a = (3 * (float)Math.Sqrt(3) *
(float)Math.Pow(r, 2)) / 4;
return a;
}
// Driver code
public static void Main()
{
float r = 5;
Console.WriteLine("" + trapezoidarea(r));
}
}
// This code is contributed
// by inder_verma
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the biggest
// trapezoid which can be inscribed
// within the semicircle
// Function to find the area
// of the biggest trapezoid
function trapezoidarea($r)
{
// the radius cannot be negative
if ($r < 0)
return -1;
// area of the trapezoid
$a = (3 * sqrt(3) * pow($r, 2)) / 4;
return $a;
}
// Driver code
$r = 5;
echo trapezoidarea($r)."\n";
// This code is contributed
// by ChitraNayal
?>
java 描述语言
<script>
// javascript Program to find the biggest trapezoid
// which can be inscribed within the semicircle
// Function to find the area
// of the biggest trapezoid
function trapezoidarea(r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the trapezoid
var a = (3 * Math.sqrt(3)
* Math.pow(r, 2)) / 4;
return a;
}
// Driver code
var r = 5;
document.write(trapezoidarea(r).toFixed(3));
// This code contributed by Princi Singh
</script>
Output:
32.476
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