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 <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 Codeint 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 approachimport 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 codepublic 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 approachimport math# Function to return the area of# parallelogram using sides and# angle at the intersection of diagonaldef 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 sidesdef 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 diagonalsdef 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 angled1 = 3d2 = 5theta = 90# Function Callarea = Area_Parallelogram3(d1, d2, theta)# Print the areaprint(round(area, 2)) |
C#
// C# program for // the above approachusing 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 codepublic 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
<script>// Javascript program for the// above approachfunction 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 diagonalfunction 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 sidesfunction 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 diagonalsfunction 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 anglelet d1 = 3;let d2 = 5;let theta = 90;// Function calllet area = Area_Parallelogram3(d1, d2, theta);// Print the areadocument.write(area);// This code is contributed by Mayank Tyagi </script> |
Output:
7.5
Time Complexity: O(1)
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
