# 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++

 `// 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`

Output:

```7.5

```

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

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Improved By : offbeat, Rajput-Ji, rutvik_56

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