To find the intersection of two area features, select both features with the digitizer tool. Then select Find Intersection of Selected Area Features from Crop/ Combine/ Split Functions in the Digitizer menu or context menu.
This operation will
create a new area feature from the intersection of the two selected area
features. There is also an option to create new area features from what
is left outside of the intersection (in the prompt below).
With the No option, new area features will be created representing the area of intersection, and the original features will remain as they were.