PDF when sampling from Rectangular Area Lights
The correct PDF for an area light is indeed $1/A$. The reason why you see the area term at the top is because you are importance sampling the light, meaning you need to divide by its PDF. This is a Monte Carlo estimator with one sample. Shirley simplifies this by simply writing $1/(1/A) = A$.

I am not sure how he got the $1 / \frac{\|V_1 \times V_2\|}{2}$.