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According to the United States Census Bureau, the city has a total area of 6.5 km² (2.5 mi²). 6.2 km² (2.4 mi²) of it is land and 0.3 km² (0.1 mi²) of it is water. The total area is 4.00% water.
The city's borders form a rectangle, nearly a square. The Otter Creek river travels north through the town. In the middle of town is a tall falls, at 37 feet, with a large, infrequently flooding basin.
The City of Vergennes was established in 1788. It is one of the oldest established cities in the United States, and also one of the smallest. The motive of a city form of municipal government is said to have been to provide a vision for building the area as an industrial center. The Otter Creek Falls and close access to the Lake Champlain waterway was thought to a fertile place for commercial growth.
Vergennes was the original but unlasting location of the state's capital. The city's chance of expansion ended about the same time relations with Britain turned to war. Commodore Thomas MacDonough made the Otter Creek falls basin the location of his naval base. From there he built ships which later won the battle at Plattsburgh Bay.
Industry boomed in the late nineteenth century, specifically a shipping industry connected to the Champlain Canal and wood-finishing related to lumber coming from Canada.
The twentieth century saw dwindling of large business, narrowing down to a few surviving companies.
As of the census of 2000, there are 2,741 people, 979 households, and 632 families residing in the city. The population density is 441.0/km² (1,141.1/mi²). There are 1,032 housing units at an average density of 166.0/km² (429.6/mi²). The racial makeup of the city is 93.43% White, 2.01% African American, 0.22% Native American, 0.36% Asian, 0.04% Pacific Islander, 1.06% from other races, and 2.88% from two or more races. 2.92% of the population are Hispanic or Latino of any race.
There are 979 households out of which 34.3% have children under the age of 18 living with them, 48.8% are married couples living together, 11.6% have a female householder with no husband present, and 35.4% are non-families. 28.2% of all households are made up of individuals and 12.5% have someone living alone who is 65 years of age or older. The average household size is 2.47 and the average family size is 3.02.
In the city the population is spread out with 28.4% under the age of 18, 13.1% from 18 to 24, 27.8% from 25 to 44, 19.3% from 45 to 64, and 11.3% who are 65 years of age or older. The median age is 33 years. For every 100 females there are 100.4 males. For every 100 females age 18 and over, there are 93.8 males.
The median income for a household in the city is $37,763, and the median income for a family is $48,155. Males have a median income of $33,669 versus $20,527 for females. The per capita income for the city is $15,465. 17.0% of the population and 8.1% of families are below the poverty line. Out of the total people living in poverty, 8.5% are under the age of 18 and 16.0% are 65 or older.