
MHB Master
#1
February 19th, 2015,
19:31
Hello!!
We have a triangle with vertices $(0, 0, 0), (1, 1, 1)$ and $(0, 2, 3)$. We want to find the area.
How could we find it?? Do we maybe use the fact that the area of the triangle is the half of the area of the parallelogram??
How do we know that it stands?? How can we justify it??

February 19th, 2015 19:31
# ADS
Circuit advertisement

MHB Journeyman
#2
February 19th, 2015,
19:41
Yes, that is correct, using the fact that the area of a parallelogram can be calculated by the magnitude of its cross product. Regarding justifying that the area of a triangle is half the area of a parallelogram I think requires a geometric proof:

MHB Apprentice
#3
February 19th, 2015,
19:43
Originally Posted by
mathmari
How could we find it?? Do we maybe use the fact that the area of the triangle is the half of the area of the parallelogram??
Sounds like a good idea. Follow these steps.

#4
February 19th, 2015,
19:58
Another option could be to work out the length of each segment (using Pythagoras), then the area can be found using Heron's Formula.
But the vector method is much quicker

Pessimist Singularitarian
#5
February 19th, 2015,
20:07
You could also use the formula developed here: