# Find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2).

1. Mar 16, 2012

### kingkong69

find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2)
its 4 d

Im confused

2. Mar 16, 2012

### emailanmol

Re: find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2

OMG! i have never seen something like this before.

Where did you find this question?
You will have to define the 4d space first.

Is the 4th dimension time? Like the Minkowski space.

A google search on area of triangle in 4d yields nothing.

3. Mar 16, 2012

### kingkong69

Last edited by a moderator: May 5, 2017
4. Mar 16, 2012

### emailanmol

5. Mar 16, 2012

### kingkong69

6. Mar 16, 2012

### emailanmol

Re: find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2

Its stated in that webpage.

the fourth co-ordinate is n which signifies the axis.

I cannot elaborate much on how you will attempt the problem as I have no experience regarding maplesoft.

I hope the link helps you with what the four co-ordinates signify

7. Mar 16, 2012

### minio

Re: find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2

I would say, that you just need to find length of each side in 4D. From there it is just ordinary triangle.

8. Mar 16, 2012

### emailanmol

How do we find length of each side in 4d?
I think I am learning something new here :-)

9. Mar 16, 2012

### minio

Re: find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2

I am definitely no expert so I might be wrong, but I would say that the length would be

$\left|AB\right|=\sqrt{(a_{w}-b_{w})^{2}+(a_{x}-b_{x})^{2}+(a_{y}-b_{y})^{2}+(a_{z}-b_{z})^{2}}$

10. Mar 16, 2012

### emailanmol

Re: find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2

Ok.I think its right by symmetricity.

But my opinion is that its not valid on this question.
Here the 4th coordinate doesnt signify the presence of a 4th dimension. It just represents some co-ordinate axis which the website states.
It is actually stating the coordinates based on some conventions.

11. Mar 16, 2012

### dodo

Re: find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2

If you call your three points A=(-1 2 -1 2), B=(-1 2 -1 1) and C=(2 -1 2 2), try to think in terms of the vectors AB and AC (as two of the sides of your triangle). The first thing you may notice is that these two vectors are orthogonal.
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