What term describes areas adjacent to your area of responsibility that extend into enemy territories?

The term that accurately describes areas adjacent to your area of responsibility that extend into enemy territories is "Area of Interest." This term encompasses not only the territory where your forces are directly operating but also the surrounding areas that could impact your operations, including enemy territories. By defining an Area of Interest, commanders gain situational awareness and insights into potential threats or opportunities that may arise from adjacent areas, thus enhancing their operational planning and decision-making.

An Area of Engagement typically refers to the specific location where combat operations occur, not necessarily adjacent territories. An Area of Operations outlines the geographic space where a unit is assigned to conduct specific missions, focusing more on the unit's direct area of responsibility rather than adjacent enemy-held regions. An Area of Surveillance pertains to regions monitored for threats or activity but does not specifically imply an extension into enemy territories.