Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How do you find the area of a triangle in a 3 dimensional graph? Is it any different than a regular 2d graph? How would you solve it, if these were your three points? A(1,-4,-2), B(3,-3,-3), C(5,-1,-2)? Thanks for any help!

share|cite|improve this question
The area of a triangle is always $bh\over 2$. If it is actually a spherical sector or some non-plane bounded by a triangle, the area changes. So you only need to find the lengths of the sides and some way of identifying the base and the height. – abiessu Sep 28 '13 at 2:41
up vote 2 down vote accepted

If you know what a vector cross product is, just take half of the magnitude of the cross product of the vectors $AB$ and $AC$.

share|cite|improve this answer

So solution is

$\text{Area} = 2.693$

$\text{Sides}: a = 3,\ b = 5,\ c = 2.449$

Using $3D$ triangle calculator:

Answer by Ross Millikan is the best algorithm to solve this.

share|cite|improve this answer

Heron's formula gives you the area of a triangle from the length of the sides. Let the sides be $a,b,c$ and $s=\frac{a+b+c}2$ then the area $A=\sqrt{s(s-a)(s-b)(s-c)}$. Works in any dimension.

share|cite|improve this answer

Let $M$ be the matrix with column vectors $C-A$ and $C -B$. Then $|\det(M^tM)|$ is the area of the parallelogram spanned by the column vectors of $M$. Works in any dimension.


share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.