# Finding Triangle Area using Cross Product

by the7joker7
Tags: cross, product, triangle
 P: 115 1. The problem statement, all variables and given/known data Find the area of a triangle PQR, where P=(0,4,4), Q=(2,-6,-5), and R=(-3,-5,6) 3. The attempt at a solution The vector PQ = (2, -10, -9) The vector PR = (-3, -9, 2) Using matrixes I set up something that looks like this... I J K 2 -10 -9 -3 -9 2 Then using the matrix methods I get. I(-20 - 81) - J(4 - 27) + K(-18 - 30) I(-101) - J(-23) + K(48) I take the square root of the squares and get. 109.4349122 Answer = 57.0832725061 What's the problem?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,301 The area of a parallelogram formed by two vectors, $\vec{u}$ and $\vec{v}$, is $|\vec{u}\times\vec{v}|$. Since a triangle is half a parallelogram, the the area of a triangle having sides $\vec{u}$ and $\vec{v}$ is half that.
$$\sqrt{(-101)^2 + (23)^2 + (-48)^2}= 114.167 ~ /2 = 57.0833$$