Skip to content
Related Articles

Related Articles

Improve Article
Find area of parallelogram if vectors of two adjacent sides are given
  • Last Updated : 14 Apr, 2021

Given two vectors in form of (xi+yj+zk) of two adjacent sides of a parallelogram. The task is to find out the area of a parallelogram.
Example: 
 

Input: 
x1 = 3, y1 = 1, z1 = -2 
x2 = 1, y2 = -3, z2 = 4
Output: Area = 17.3205081 
Input: 
x1 = 1, y1 = 3, z1 = 2 
x2 = 1, y2 = -3, z2 = 4
Output: Area = 19.078784028338912
 

 

 



Approach: Suppose we have two vectors a(x1*i+y1*j+z1*k) and b(x2*i+y2*j+z2*k) and we know that area of parallelogram is given by : 
 

Area of parallelogram = magnitude of cross product of vectors a and b i.e |axb| 
And we know a X b = (y1*z2 – y2*z1)*i – (x1*z2 – x2*z1)*j + (x1*y2 – x2*y1)*k
Then area = 
\hug{\sqrt{(y_{1}*z_{2}-y_{2}*z_{1})^{2}+(x_{1}*z_{2}-x_{2}*z_{1})^{2}+(x_{1}*y_{2}-x_{2}*y_{1})^{2}}

 

C++




// C++ code to calculate area of
// parallelogram if vectors of
// 2 adjacent sides are given
 
#include<bits/stdc++.h>
using namespace std ;
 
// Function to calculate area of parallelogram 
float area(float x1, float y1, float z1, float x2,
            float y2, float z2)
    {
        float area = sqrt(pow((y1 * z2 - y2 * z1),2)
                        + pow((x1 * z2 - x2 * z1),2) +
                         pow((x1 * y2 - x2 * y1),2));
        return area;
    }
     
// Driver Code
int main()
{
    float x1 = 3;
    float y1 = 1;
    float z1 = -2;
    float x2 = 1;
    float y2 = -3;
    float z2 = 4;
    float a = area(x1, y1, z1, x2, y2, z2);
    cout << "Area = " << a;
    return 0;
// This code is contributed
// by Amber_Saxena.
}

Java




// Java code to calculate area of 
// parallelogram if vectors of
// 2 adjacent sides are given
 
public class GFG {
     
    // Function to calculate area of parallelogram  
    static float area(float x1, float y1, float z1, float x2,
                float y2, float z2)
        
            float area =(float) Math.sqrt(Math.pow((y1 * z2 - y2 * z1),2)
                            + Math.pow((x1 * z2 - x2 * z1),2) +
                             Math.pow((x1 * y2 - x2 * y1),2));
            return area;
        
 
    // Driver code
    public static void main (String args[]){
         float x1 = 3;
            float y1 = 1;
            float z1 = -2;
            float x2 = 1;
            float y2 = -3;
            float z2 = 4;
            float a = area(x1, y1, z1, x2, y2, z2);
            System.out.println("Area = " + a) ;
           
    }
 
// This code is contributed by ANKITRAI1
}

Python




# Python code to calculate area of
# parallelogram if vectors of
# 2 adjacent sides are given
 
import math
 
# to calculate area of parallelogram
def area(x1, y1, z1, x2, y2, z2):
    area = math.sqrt((y1 * z2 - y2 * z1) ** 2
           + (x1 * z2 - x2 * z1) ** 2 +
           (x1 * y2 - x2 * y1) ** 2)
    return area
 
# main function
def main():
    x1 = 3
    y1 = 1
    z1 = -2
    x2 = 1
    y2 = -3
    z2 = 4
    a = area(x1, y1, z1, x2, y2, z2)
    print("Area = ", a)
 
# driver code   
if __name__=="__main__":
    main()

C#




// C# code to calculate area of
// parallelogram if vectors of
// 2 adjacent sides are given
using System;
 
class GFG
{
 
// Function to calculate area
// of parallelogram
static float area(float x1, float y1,
                  float z1, float x2,
                  float y2, float z2)
{
    float area = (float) Math.Sqrt(Math.Pow((y1 * z2 - y2 * z1), 2) +
                                   Math.Pow((x1 * z2 - x2 * z1), 2) +
                                   Math.Pow((x1 * y2 - x2 * y1), 2));
    return area;
}
 
// Driver code
public static void Main ()
{
    float x1 = 3;
    float y1 = 1;
    float z1 = -2;
    float x2 = 1;
    float y2 = -3;
    float z2 = 4;
    float a = area(x1, y1, z1, x2, y2, z2);
    Console.Write("Area = " + a) ;
}
}
 
// This code is contributed
// by ChitraNayal

PHP




<?php
// PHP code to calculate area of
// parallelogram if vectors of
// 2 adjacent sides are given
 
// Function to calculate area
// of parallelogram
function area($x1, $y1, $z1,
              $x2, $y2, $z2)
{
        $area = sqrt(pow(($y1 * $z2 - $y2 * $z1), 2) +
                     pow(($x1 * $z2 - $x2 * $z1), 2) +
                     pow(($x1 * $y2 - $x2 * $y1), 2));
        return $area;
}
     
// Driver Code
$x1 = 3; $y1 = 1; $z1 = -2;
$x2 = 1; $y2 = -3; $z2 = 4;
$a = area($x1, $y1, $z1,
          $x2, $y2, $z2);
echo ("Area = ");
echo ($a);
     
// This code is contributed
// by Shivi_Aggarwal
?>

Javascript




<script>
 
// Javascript code to calculate area of
// parallelogram if vectors of
// 2 adjacent sides are given
 
// Function to calculate area
// of parallelogram
function area(x1, y1, z1,
              x2, y2, z2)
{
        area = Math.sqrt(Math.pow((y1 * z2 - y2 * z1), 2) +
                     Math.pow((x1 * z2 - x2 * z1), 2) +
                     Math.pow((x1 * y2 - x2 * y1), 2));
        return area;
}
     
// Driver Code
let x1 = 3;
let y1 = 1;
let z1 = -2;
let x2 = 1;
let y2 = -3;
let z2 = 4;
a = area(x1, y1, z1,
          x2, y2, z2);
document.write ("Area = ");
document.write (a);
     
// This code is contributed by Bobby
 
</script>
Output: 
Area =  17.320508075688775

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live




My Personal Notes arrow_drop_up
Recommended Articles
Page :