计算给定边长的循环四边形的面积
给定四个正整数 A 、 B 、 C 和 D 表示一个循环四边形的边长，任务是求循环四边形的面积。
示例:
输入: A = 10，B = 15，C = 20，D = 25 T3】输出: 273.861
输入: A = 10，B = 30，C = 50，D = 20 T3】输出: 443.706
方法:给定的问题可以基于以下观察来解决:
- 循环四边形是顶点都在一个圆上的四边形。这个圆被称为外接圆或外接圆，顶点被称为共圆。
- 上图中 r 为外接圆半径， A 、 B 、 C 、 D 分别为边长 PQ 、 QR 、 RS 、 SP 。
- 四边形的面积由 给出，布雷施耐德公式 为:
其中，A、B、C 和 D 是三角形的边， α和γ是四边形的对角。
因为，四边形的对角之和是 180 度。因此，cos(180/2) = cos(90) = 0 的值。
因此，求面积的公式简化为
。
。因此，想法是将
的值打印为给定四边形的合成面积。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the area
// of cyclic quadrilateral
float calculateArea(float A, float B,
float C, float D)
{
// Stores the value of
// half of the perimeter
float S = (A + B + C + D) / 2;
// Stores area of cyclic quadrilateral
float area = sqrt((S - A) * (S - B)
* (S - C) * (S - D));
// Return the resultant area
return area;
}
// Driver Code
int main()
{
float A = 10;
float B = 15;
float C = 20;
float D = 25;
cout << calculateArea(A, B, C, D);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program for the above approach
import java.io.*;
class GFG{
// Function to find the area
// of cyclic quadrilateral
static float calculateArea(float A, float B,
float C, float D)
{
// Stores the value of
// half of the perimeter
float S = (A + B + C + D) / 2;
// Stores area of cyclic quadrilateral
float area = (float)Math.sqrt((S - A) * (S - B) *
(S - C) * (S - D));
// Return the resultant area
return area;
}
// Driver code
public static void main (String[] args)
{
float A = 10;
float B = 15;
float C = 20;
float D = 25;
System.out.println(calculateArea(A, B, C, D));
}
}
// This code is contributed by Ankita saini
Python 3
# Python3 program for the above approach
from math import sqrt
# Function to find the area
# of cyclic quadrilateral
def calculateArea(A, B, C, D):
# Stores the value of
# half of the perimeter
S = (A + B + C + D) // 2
# Stores area of cyclic quadrilateral
area = sqrt((S - A) * (S - B) *
(S - C) * (S - D))
# Return the resultant area
return area
# Driver Code
if __name__ == '__main__':
A = 10
B = 15
C = 20
D = 25
print(round(calculateArea(A, B, C, D), 3))
# This code is contributed by mohit kumar 29
C
// C# program for the above approach
using System;
class GFG{
// Function to find the area
// of cyclic quadrilateral
static float calculateArea(float A, float B,
float C, float D)
{
// Stores the value of
// half of the perimeter
float S = (A + B + C + D) / 2;
// Stores area of cyclic quadrilateral
float area = (float)Math.Sqrt((S - A) * (S - B) *
(S - C) * (S - D));
// Return the resultant area
return area;
}
// Driver Code
static public void Main()
{
float A = 10;
float B = 15;
float C = 20;
float D = 25;
Console.Write(calculateArea(A, B, C, D));
}
}
// This code is contributed by code_hunt
java 描述语言
<script>
// java script program for the above approach
// Function to find the area
//of cyclic quadrilateral
function calculateArea(A, B, C, D){
//Stores the value of
// half of the perimeter
let S = (A + B + C + D) /2
// Stores area of cyclic quadrilateral
let area = Math.sqrt((S - A) * (S - B) *
(S - C) * (S - D))
//Return the resultant area
return area;
}
// Driver Code
let A = 10;
let B = 15;
let C = 20;
let D = 25;
document.write(calculateArea(A, B, C, D).toFixed(3))
//this code is contributed by sravan kumar
</script>
Output:
273.861
时间复杂度:O(1) T5辅助空间:** O(1)
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