Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 2 / 2 / Solution

The boundary order fixes the orientation. Two edges issuing from $A$ are $\overrightarrow{AB}=(0,0,1)$ and $\overrightarrow{AD}=(1,1,0)$. Their cross product gives the oriented vector area:Its norm is $\sqrt{2}$, the ordinary rectangle area. The sign agrees with traversing $A\to B\to C\to D\to A$ by the right-hand orientation rule.