The question "What were the three regions of unit states?" appears to reflect a misunderstanding. The United States is a single country in North America—not divided into three "regions of united states" in any standard geographic, political, or historical framework.
Census Bureau (4): Northeast, Midwest, South, West (9 divisions).
Federal Reserve (12): Districts.
Court of Appeals (13): Circuits.
Cultural/vernacular: New England, Mid-Atlantic, South, Midwest, Southwest, West, Pacific Northwest, etc.
The Western Hemisphere is sometimes divided into North America, Central America, South America—but the United States is one country within North America.
There is no canonical "three regions of the United States." Clarifying the intended context—historical, geographic, political, cultural—would yield a meaningful answer. The United States itself is a federal republic of 50 states, one federal district, and several territories, located in North America.