Consider the tetrahedron in the image:
Prove that the volume of the tetrahedron is given by $\frac16 |a \times b \cdot c|$.
I know volume of the tetrahedron is equal to the base area times height, and here, the height is $h$, and I’m considering the base area to be the area of the triangle $BCD$.
So, what I have is:
$$\begin{align} \text{base area} &= \frac12 \lvert a \times b \rvert \\ \text{height $h$} &= \lvert c\rvert \cos \theta \end{align}$$
So volume is $$V=\frac12 \lvert a \times b\rvert \cdot \lvert c\rvert \cos \theta $$
But I don’t know how to arrive from this at $\frac16 |a \times b \cdot c|$.
Please advise.