# How to calculate the area of a 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don’t know how to calculate area in 3d. I have developed data as follows.

(119.91227722167969, 122.7717056274414, 39.3568115234375),
(119.8951187133789, 122.7717056274414, 39.38057327270508),
(121.11941528320312, 123.2818832397461, 38.41301345825195)


$$S=\dfrac{|\mathbf{AB}\times\mathbf{AC}|}2=\dfrac{|\mathbf{AB}||\mathbf{AC}||\sin(\theta)|}2 S=\dfrac{|\mathbf{AB}\times\mathbf{AC}|}2=\dfrac{|\mathbf{AB}||\mathbf{AC}||\sin(\theta)|}2$$
that is (see the Wikipedia link to get the cross-product in $$\mathbb{R}^3\mathbb{R}^3$$) :
$$S=\frac 12 \sqrt{(y_{AB}\cdot z_{AC}-z_{AB}\cdot y_{AC})^2+(z_{AB}\cdot x_{AC}-x_{AB}\cdot z_{AC})^2+(x_{AB}\cdot y_{AC}-y_{AB}\cdot x_{AC})^2}S=\frac 12 \sqrt{(y_{AB}\cdot z_{AC}-z_{AB}\cdot y_{AC})^2+(z_{AB}\cdot x_{AC}-x_{AB}\cdot z_{AC})^2+(x_{AB}\cdot y_{AC}-y_{AB}\cdot x_{AC})^2}$$
if $$\mathbf{AB}=(x_{AB},y_{AB},z_{AB})\mathbf{AB}=(x_{AB},y_{AB},z_{AB})$$ and $$\mathbf{AC}=(x_{AC},y_{AC},z_{AC})\mathbf{AC}=(x_{AC},y_{AC},z_{AC})$$