Calculate Area of Triangle in 3D with Given Vertices | Homework Solution

In summary, the conversation discusses finding the area of a triangle given three vertices. The method of finding the area using a determinant is incorrect and instead, the area can be found using the formula A=1/2 * base * height or by finding the length of the cross product of two difference vectors along the edges of the triangle. A visual representation may be helpful in solving this problem.
  • #1
abrowaqas
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Homework Statement


The vertices of triangle are (2,0,0) ; (0,3,0) ; (0,0,6) . Find the area of triangle.


Homework Equations





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) .
 
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  • #2
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 [tex] A= \frac{1}{2} *base*height[/tex]You have points so you can find the lengths of the base and height.

A quick sketch may be needed.
 
  • #3
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.
 

1. What is the formula for finding the area of a triangle in 3D?

The formula for finding the area of a triangle in 3D is 1/2 * base * height, where base and height are the measurements of the triangle's base and height in three-dimensional space.

2. How is the area of a triangle in 3D different from a 2D triangle?

The area of a triangle in 3D takes into account the third dimension, or depth, of the triangle. This means that the formula for finding the area must include a measurement for both the base and height in three-dimensional space, rather than just the base and height in a 2D triangle.

3. Can the area of a triangle in 3D be negative?

No, the area of a triangle in 3D cannot be negative. The area is a measurement of space, and therefore cannot have a negative value.

4. How can the area of a triangle in 3D be used in real-world applications?

The area of a triangle in 3D can be used in various real-world applications, such as calculating the surface area of a three-dimensional object or determining the volume of a pyramid or cone. It can also be used in physics and engineering to calculate the moment of inertia, which is important in understanding the stability and motion of objects.

5. Are there any other methods for finding the area of a triangle in 3D?

Yes, there are other methods for finding the area of a triangle in 3D, such as using vectors or the cross product. These methods involve using mathematical concepts and equations to calculate the area. However, the basic formula of 1/2 * base * height is the most commonly used and easiest to understand method for finding the area of a triangle in 3D.

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