# Homework Help: Area of Triangle in 3D

1. Aug 22, 2010

### abrowaqas

1. The problem statement, all variables and given/known data
The vertices of triangle are (2,0,0) ; (0,3,0) ; (0,0,6) . Find the area of triangle.

2. Relevant equations

3. The attempt at a solution
is it right that i put in determinant like
Area of triangle =
0.5 | 2 0 0 |
| 0 3 0 |
| 0 0 6 |
= 0.5 (2* 3 * 6)
= 18 .

but i think this method is wrong ... the answer of this question is 3 sqrt ( 14) .

2. Aug 22, 2010

### ╔(σ_σ)╝

In your approach what you are doing is not the area of a triangle.

You are actually finding the volume of a parallelepiped.

The area of the triangle will always be $$A= \frac{1}{2} *base*height$$

You have points so you can find the lengths of the base and height.

A quick sketch may be needed.

3. Aug 22, 2010

### Dick

It's also half the length of the cross product of two difference vectors along the edges of the triangle. You can use a determinant type form to work out the cross product.