# Area of a Triangle

1. May 26, 2008

### jesuslovesu

1. The problem statement, all variables and given/known data

The three vectors A, B, C point from the origin O to the three corners of a triangle. Show that the area of a triangle = 1/2 |( BxC + CxA + AxB )|

2. Relevant equations

1/2 |a x b| = 1/2 |a||b|sin(alpha)

3. The attempt at a solution

My initial attempt at this problem was to take the cross product like (Bx, By, Bz) x (Cx, Cy, Cz) and seeing if anything canceled. Unfortunately nothing did (I also tried with a '2d' vector (Bx, By, 0) etc and nothing canceled either).

I believe I have to somehow use the equation I listed, but I'm not really sure what to do. It seems a little counterproductive to do the cross product three times. There aren't any simplifications that I can see. Anyone know where I should start?

2. May 26, 2008

### rock.freak667

For a triangle of side |a| and |b| with included angle $, what does [itex]\frac{1}{2} |a||b|sin\alpha$ give?

3. May 26, 2008

### tiny-tim

Hi jesuslovesu!

Hint: what is the area of triangle OAB?