Hamilton Mathematical Olympiad 2021 Q4

$ABCD$ is a rectangle with area 6 cm$^2$.The point $E$ lies on $AB$, $F$ lies on $BC$, $G$ lies on $CD$ and $H$ lies on $DA$. The point $I$ lies on $AC$ and is the point of intersection of $EG$ and $FH$, and $AEIH$ and $IFCG$ are both rectangles. One possible diagram is shown below.

Given that the combined area of $AEIH$ and $IFCG$ is 4 cm$^2$, find the two possible values for the area of rectangle $AEIH$ in cm$^2$.