程序计算平行四边形的面积

给定整数A和B表示平行四边形的边长， Y 即平行四边形的对角线D1和D2的边和长度之间的角度以及对角线的相交处的角度为0 ，任务是从提供的信息中找到平行四边形的面积。

A parallelogram is a type of quadrilateral that has equal and parallel opposite sides and angle between them is not right angle.

例子：

Input: A = 6, B = 10, 0 = 30
Output: 18.48
Explanation:
For the given sides 6 and 10 and for the angle 30 degree the area of parallelogram will be 18.48.

Input: A = 3, B = 5, Y = 45
Output: 10.61
Explanation:
For the given sides 3 and 5 and for the angle 45 degree the length of diagonal will be 10.61.

Input: D1 = 3, D2 = 5, 0 = 90
Output: 7.5
Explanation:
For the given diagonals 3 and 5 and for the angle 90 degree the area of parallelogram will be 7.5.

方法：可以通过以下三个公式来计算平行四边形的面积：

• 从给定的A边和B边以及对角线之间的角度，可以通过以下公式计算平行四边形的面积：

 Area of Parallelogram for sides and angle between diagonals = ((A² – B²) * tan 0) / 2

• 从给定的A边和B边以及两边之间的角度，可以通过以下公式计算平行四边形的面积：

Area of Parallelogram for sides and angle between sides = A * B * sin Y
 

• 从给定的对角线D1和D2的长度以及它们之间的角度，可以通过以下公式计算平行四边形的面积：

Area of Parallelogram for diagonals and angle between diagonals = (D1 * D2 * sin 0)/2

下面是上述方法的实现：

C++

// C++ program for the
// above approach
#include 
using namespace std;
 
double toRadians(int degree)
{
  double pi = 3.14159265359;
  return ((double)degree * (pi / 180));
}
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of diagonal
double Area_Parallelogram1(int a, int b,
                           int theta)
{
  
    // Calculate area of parallelogram
    double area = (abs(tan(toRadians(theta))) / 2) *
                   abs(a * a - b * b);
  
    // Return the answer
    return area;
}
  
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of sides
double Area_Parallelogram2(int a, int b,
                           int gamma)
{    
  // Calculate area of parallelogram
  double area = (abs(sin(toRadians(gamma)))) *
                 abs(a * b);
 
  // Return the answer
  return area;
}
  
// Function to return the area of
// parallelogram using diagonals and
// angle at the intersection of diagonals
static double Area_Parallelogram3(int d1, int d2,
                                  int theta)
{    
  // Calculate area of parallelogram
  double area = (abs(sin(toRadians(theta))) / 2) *
                 abs(d1 * d2);
 
  // Return the answer
  return area;
}
 
  
// Driver Code
int main()
{
  // Given diagonal and angle
  int d1 = 3;
  int d2 = 5;
  int theta = 90;
 
  // Function call
  double area = Area_Parallelogram3(d1,
                                    d2,
                                    theta);
   
  // Print the area
  printf("%.2f", area);
}
 
// This code is contributed by rutvik_56

Java

// Java program for above approach
import java.io.*;
 
class GFG{
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of diagonal
static double Area_Parallelogram1(int a, int b,
                                  int theta)
{
 
    // Calculate area of parallelogram
    double area = (Math.abs(Math.tan(
                   Math.toRadians(theta))) / 2) *
                   Math.abs(a * a - b * b);
 
    // Return the answer
    return area;
}
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of sides
static double Area_Parallelogram2(int a, int b,
                                  int gamma)
{
     
    // Calculate area of parallelogram
    double area = (Math.abs(Math.sin(
                   Math.toRadians(gamma)))) *
                   Math.abs(a * b);
 
    // Return the answer
    return area;
}
 
// Function to return the area of
// parallelogram using diagonals and
// angle at the intersection of diagonals
static double Area_Parallelogram3(int d1, int d2,
                                  int theta)
{
     
    // Calculate area of parallelogram
    double area = (Math.abs(Math.sin(
                   Math.toRadians(theta))) / 2) *
                   Math.abs(d1 * d2);
 
    // Return the answer
    return area;
}
 
// Driver code
public static void main (String[] args)
{
     
    // Given diagonal and angle
    int d1 = 3;
    int d2 = 5;
    int theta = 90;
     
    // Function call
    double area = Area_Parallelogram3(
                  d1, d2, theta);
     
    // Print the area
    System.out.format("%.2f", area);
}
}
 
// This code is contributed by offbeat

Python3

# Python3 program for the above approach
 
import math
 
# Function to return the area of
# parallelogram using sides and
# angle at the intersection of diagonal
def Area_Parallelogram1(a, b, theta):
 
    # Calculate area of parallelogram
    area = (abs(math.tan(math.radians(theta)))/2) \
           * abs(a**2 - b**2)
 
    # Return the answer
    return area
 
# Function to return the area of
# parallelogram using sides and
# angle at the intersection of sides
def Area_Parallelogram2(a, b, gamma):
 
    # Calculate area of parallelogram
    area = (abs(math.sin(math.radians(gamma)))) \
            * abs(a * b)
 
    # Return the answer
    return area
 
# Function to return the area of
# parallelogram using diagonals and
# angle at the intersection of diagonals
def Area_Parallelogram3(d1, d2, theta):
 
    # Calculate area of parallelogram
    area = (abs(math.sin(math.radians(theta)))/2) \
            * abs(d1 * d2)
 
    # Return the answer
    return area
 
 
# Driver Code
 
# Given diagonal and angle
d1 = 3
d2 = 5
theta = 90
 
# Function Call
area = Area_Parallelogram3(d1, d2, theta)
# Print the area
print(round(area, 2))

C#

// C# program for
// the above approach
using System;
class GFG{
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of diagonal
static double Area_Parallelogram1(int a, int b,
                                  int theta)
{
  // Calculate area of parallelogram
  double area = (Math.Abs(Math.Tan((theta *
                          Math.PI) / 180)) / 2) *
                 Math.Abs(a * a - b * b);
 
  // Return the answer
  return area;
}
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of sides
static double Area_Parallelogram2(int a, int b,
                                  int gamma)
{   
  // Calculate area of parallelogram
  double area = (Math.Abs(Math.Sin((gamma *
                          Math.PI) / 180))) *
                 Math.Abs(a * b);
 
  // Return the answer
  return area;
}
 
// Function to return the area of
// parallelogram using diagonals and
// angle at the intersection of diagonals
static double Area_Parallelogram3(int d1, int d2,
                                  int theta)
{   
  // Calculate area of parallelogram
  double area = (Math.Abs(Math.Sin((theta *
                          Math.PI) / 180)) / 2) *
                 Math.Abs(d1 * d2);
 
  // Return the answer
  return area;
}
 
// Driver code
public static void Main(String[] args)
{
  // Given diagonal and angle
  int d1 = 3;
  int d2 = 5;
  int theta = 90;
 
  // Function call
  double area = Area_Parallelogram3(d1, d2, theta);
 
  // Print the area
  Console.Write("{0:F2}", area);
}
}
 
// This code is contributed by Rajput-Ji

Javascript

 
// Javascript program for the
// above approach
function toRadians(degree)
{
    let pi = 3.14159265359;
    return (degree * (pi / 180));
}
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of diagonal
function Area_Parallelogram1(a, b,
                             theta)
{
     
    // Calculate area of parallelogram
    let area = (Math.abs(Math.tan(toRadians(theta))) / 2) *
                Math.abs(a * a - b * b);
 
    // Return the answer
    return area;
}
 
// Function to return the area of
// parallelogram using sides and
// angle at the intersection of sides
function Area_Parallelogram2(a, b,
                             gamma)
{   
     
    // Calculate area of parallelogram
    let area = (Math.abs(Math.sin(toRadians(gamma)))) *
                         Math.abs(a * b);
     
    // Return the answer
    return area;
}
 
// Function to return the area of
// parallelogram using diagonals and
// angle at the intersection of diagonals
function Area_Parallelogram3(d1, d2,
                             theta)
{   
     
    // Calculate area of parallelogram
    let area = (Math.abs(Math.sin(toRadians(theta))) / 2) *
                         Math.abs(d1 * d2);
     
    // Return the answer
    return area;
}
 
// Driver Code
 
// Given diagonal and angle
let d1 = 3;
let d2 = 5;
let theta = 90;
 
// Function call
let area = Area_Parallelogram3(d1, d2,
                               theta);
 
// Print the area
document.write(area);
 
// This code is contributed by Mayank Tyagi
     

输出：

7.5

时间复杂度： O(1)
辅助空间： O(1)