Final answer:
The fish-scale armor was a Han Dynasty invention that improved military technology, enabling the production of enhanced protective gear for soldiers.
Step-by-step explanation:
The Han Dynasty invention that improved the area of society related to military technology was fish-scale armor. This type of armor was an advancement in protective military gear, which further enhanced the effectiveness of soldiers in combat. The invention and proliferation of effective ironworking techniques by the Han allowed for the mass production of various tools and weapons, including improved armor. Developments like the fish-scale armor contributed to the Han military's prowess and were a part of the larger historical context of technological innovations that included advancements in agriculture, military strategy, and domestic implements.