Program to calculate area of a parallelogram

Given integers A and B denoting the length of sides of a parallelogram and Y that is the angle between the sides and length of diagonals D1 and D2 of the parallelogram and an angle 0 at the intersection of the diagonal, the task is to find the area of the parallelogram from the information provided.

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

Examples:

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.

Approach: The area of the parallelogram can be calculated by the following three formulas:

• From given sides A and B and the angle between the diagonals, the area of the parallelogram can be calculated by the following formula:

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

• From given sides A and B and the angle between the sides, the area of the parallelogram is can be calculated by the following formula: 
   

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

• From the given length of diagonals D1 and D2 and the angle between them, the area of the parallelogram can be calculated by the following formula: 
   

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

Below is the implementation of the above approach:

// C++ program for the 
// above approach
#include <bits/stdc++.h>
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 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 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# 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 

<script>

// 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
    
</script>

7.5

Time Complexity: O(1)
Auxiliary Space: O(1)