计算梯形高度的程序

给定两个整数a和b代表两个底边的长度，两个整数p1和p2代表梯形的非平行边，任务是找到梯形的高度。

A Trapezoid is a convex quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides which are not parallel are referred to as the legs. There can also be a pair of bases. 
In the figure, CD || AB. Therefore, they form the bases, and the other two sides i.e., AD and BC form the legs.

例子：

Input: a = 14, b = 13, p1 = 25, p2 = 10
Output: 11.2

Input: a = 8, b = 16, p1 = 25, p2 = 10
Output: 7.92401

方法：为求梯形的高度，在梯形底边AB上构造垂线DE和CF ，如下图所示。

现在，三角形 AED 的面积和三角形 CFB 的面积可以使用 Heron 公式计算，边为p1 、 p2和(b – a) 。此外，它的面积等于0.5 * (b – a) * h 。
根据这两个方程，计算h的值，即梯形的高度。

Heron’s Formula: Consider a triangle with sides a, b and c, then 
Area of triangle, A = (s (s – a)(s – b)(s – c))^1/2, where s = (a + b + c)/2

Also, A = 0.5 * base * height
After rearranging the terms, the height of the trapezoid = (A * 2) / Base

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to calculate height
// of the trapezoid
void findHeight(float p1, float p2,
                float b, float c)
{
    float a = max(p1, p2) - min(p1, p2);
 
    // Apply Heron's formula
    float s = (a + b + c) / 2;
 
    // Calculate the area
    float area = sqrt(s * (s - a)
                      * (s - b) * (s - c));
 
    // Calculate height of trapezoid
    float height = (area * 2) / a;
 
    // Print the height
    cout << "Height is: " << height;
}
 
// Driver Code
int main()
{
    // Given a, b, p1 and p2
    float p1 = 25, p2 = 10;
    float a = 14, b = 13;
 
    findHeight(p1, p2, a, b);
 
    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
 
class GFG
{
   
// Function to calculate height
// of the trapezoid
static void findHeight(float p1, float p2,
                float b, float c)
{
    float a = Math.max(p1, p2) - Math.min(p1, p2);
 
    // Apply Heron's formula
    float s = (a + b + c) / 2;
 
    // Calculate the area
    float area = (int)Math.sqrt(s * (s - a)
                      * (s - b) * (s - c));
 
    // Calculate height of trapezoid
    float height = (area * 2) / a;
 
    // Print the height
    System.out.print("Height is: " + height);
}
 
// Driver Code
public static void main(String args[])
{
   
    // Given a, b, p1 and p2
    float p1 = 25, p2 = 10;
    float a = 14, b = 13;
 
    findHeight(p1, p2, a, b);
}
}
 
// This code is contributed by splevel62.

Python3

# Python3 program to implement
# the above approach
import math
 
# Function to calculate height
# of the trapezoid
def findHeight(p1, p2, b, c) :            
    a = max(p1, p2) - min(p1, p2)
 
    # Apply Heron's formula
    s = (a + b + c) // 2
 
    # Calculate the area
    area = math.sqrt(s * (s - a)
                      * (s - b) * (s - c))
 
    # Calculate height of trapezoid
    height = (area * 2) / a
 
    # Prthe height
    print("Height is: ",  height)
 
 
# Driver Code
 
# Given a, b, p1 and p2
p1 = 25
p2 = 10
a = 14
b = 13
 
findHeight(p1, p2, a, b)
 
# this code is contributed by sanjoy_62.

C#

// C# program to implement
// the above approach
using System;
 
public class GFG
{
   
// Function to calculate height
// of the trapezoid
static void findHeight(float p1, float p2,
                float b, float c)
{
    float a = Math.Max(p1, p2) - Math.Min(p1, p2);
 
    // Apply Heron's formula
    float s = (a + b + c) / 2;
 
    // Calculate the area
    float area = (int)Math.Sqrt(s * (s - a)
                      * (s - b) * (s - c));
 
    // Calculate height of trapezoid
    float height = (area * 2) / a;
 
    // Print the height
    Console.Write("Height is: " + height);
}
 
// Driver Code
public static void Main(String []args)
{
   
    // Given a, b, p1 and p2
    float p1 = 25, p2 = 10;
    float a = 14, b = 13;
 
    findHeight(p1, p2, a, b);
}
}
 
// This code is contributed by shikhasingrajput

输出：

Height is: 11.2

时间复杂度： O(1)
辅助空间： O(1)

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