# Find Area of Triangle (-1 2 -1 2), (-1 2 -1 1) & (2 -1 2 2)

• kingkong69
In summary, the area of the triangle with given vertices in 4D space can be calculated using the length of each side, which can be found using the formula \left|AB\right|=\sqrt{(a_{w}-b_{w})^{2}+(a_{x}-b_{x})^{2}+(a_{y}-b_{y})^{2}+(a_{z}-b_{z})^{2}}, taking into consideration the fourth coordinate as a conventional axis and not a representation of a fourth dimension.
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

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.

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

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

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

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

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

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

Ok.I think its right by symmetricity.

But my opinion is that its not valid on this question.
Here the 4th coordinate doesn't 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.

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.

## 1. How do you find the area of a triangle?

The area of a triangle can be found by using the formula A = 1/2 * base * height, where the base is the length of one side of the triangle and the height is the perpendicular distance from that side to the opposite vertex.

## 2. What are the coordinates of a triangle?

The coordinates of a triangle can be represented by three points, each with an x and y value. In the given example, the coordinates are (-1, 2), (-1, 1), and (2, -1).

## 3. How do you calculate the base and height of a triangle?

The base and height of a triangle can be found by measuring the length of one side and the perpendicular distance from that side to the opposite vertex. Alternatively, if the coordinates of the vertices are known, the base and height can be calculated using the distance formula.

## 4. How do you find the area of a triangle when given coordinates?

To find the area of a triangle when given coordinates, you can use the formula A = 1/2 * base * height. First, determine the length of one side of the triangle using the distance formula, then find the perpendicular distance from that side to the opposite vertex. Plug these values into the formula to calculate the area.

## 5. Can the coordinates of a triangle be negative?

Yes, the coordinates of a triangle can be negative. In the given example, two of the vertices have negative coordinates (-1, 2) and (-1, 1). This means that these points are located to the left and below the origin on a coordinate plane.

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