# Using the Vector Cross product to find the Area of a Triangle

Let’s see how to use the *Vector Cross product* to find the Area of a Triangle. **Here we will see that half of the magnitude of the cross product of vector AB and AC gives the area of the triangle ABC.** (reference: the image below)

Let, **AB **and** AC **are 2 vectors and these are taken as 2 adjacent sides of triangle ABC. The magnitude of **AB** and **AC** are b and a respectively, which are the length of two sides of the triangle as well.

L is the height of the triangle and θ is the angle CAB.

Hence, L = a sin θ

Area of ABC = (½) AB . L = (½) b a sin θ ………… (1)

And, |AB x AC| = b a sin θ …………… (2)

So, Area of ABC = (½) |AB x AC|

**Here we can see that half of the magnitude of the cross product of vector AB and AC gives the area of the triangle ABC.**