Chapter 6.3, Problem 6E

What is the relationship between the volume of thetetrahedron defined by the vectors
$\left[\begin{array}{l}{a}_1\\ a_2\\ 1\end{array}\right],\left[\begin{array}{l}{b}_1\\ b_2\\ 1\end{array}\right],\left[\begin{array}{l}{c}_1\\ c_2\\ 1\end{array}\right]$ and the area of the triangle with vertices $\left[\begin{array}{l}{a}_1\\ a_2\end{array}\right],\left[\begin{array}{l}{b}_1\\ b_2\end{array}\right],\left[\begin{array}{l}{c}_1\\ c_2\end{array}\right]$ ?
See Exercises 4 and 5. Explain this relationship geometrically. Hint: Consider the top face of the tetrahedron.