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# Find area of triangle if two vectors of two adjacent sides are given using C++

Suppose we have two vectors for two adjacent sides of a triangle in the form $x\hat{i}+y\hat{j}+z\hat{k}$ Our task is to find the area of triangle. The area of triangle is magnitude of the cross product of two vectors. (|A x B|)

$$\frac{1}{2}\rvert \vec{A}\times\vec{B}\rvert=\frac{1}{2}\sqrt{\lgroup y_{1}*z_{2}-y_{2}*z_{1}\rgroup^{2}+\lgroup x_{1}*z_{2}-x_{2}*z_{1}\rgroup^{2}+\lgroup x_{1}*y_{2}-x_{2}*y_{1}\rgroup^{2}}$$

## Example

#include<iostream> #include<cmath> using namespace std; float area(float A[], float B[]) { float area = sqrt(pow((A[1] * B[2] - B[1] * A[2]),2) + pow((A[0] * B[2] - B[0] * A[2]),2) + pow((A[0] * B[1] - B[0] * A[1]),2)); return area*0.5; } int main() { float A[] = {3, 1, -2}; float B[] = {1, -3, 4}; float a = area(A, B); cout << "Area = " << a; }

## Output

Area = 8.66025

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