Question: What was the 2010 population of the town near Vernon Hills which was laid out in 1857 and with a city hall designed by Charles Sumner Frost?

Context paragraphs:
American Express Building-Carroll: The American Express Building-Carroll, also known as the Carroll Express Building is a historic structure located in Carroll, Iowa, United States.  Like the Chicago & Northwestern Passenger Depot across the street, the express building is an example of a replacement station built during the Golden Age of Steam Railroading.  It replaced a frame, structure that was built sometime between 1888 and 1893.  The Chicago and North Western Railway (CNW) had built two branch lines from Carroll in 1877 and 1880, which increased business and necessitated the building of the original express building between 1883 and 1888.  Chicago architect Charles Sumner Frost designed this building, and the depot.  They are similar in design, and were both completed in 1896.  The building was listed on the National Register of Historic Places in 1990.

Navy Pier Auditorium: The Navy Pier Auditorium, designed by the architect Charles Sumner Frost and constructed in 1916, is located at the east end of Navy Pier in Chicago and is also known as the Hall.  The building's Aon Grand Ballroom measures 138 ft by 150 ft (42m x 48m) and has a 100 ft (30m) high half-domed ceiling.

Maine State Building: The Maine State Building is a historic building on Preservation Way, part of the Poland Springs resort complex in South Poland, Maine.  It was built in 1893 at the Columbian Exposition in Chicago.  Designed by Chicago architect Charles Sumner Frost, a Lewiston, Maine native and MIT graduate, the building was constructed of granite with a slate roof.  All the materials were from Maine and crafted by craftsmen and companies from Maine.  At the fair, the building was filled with displays about the State of Maine.

Lake Forest, Illinois: Lake Forest is a city located in Lake County, Illinois, United States.  As of the 2010 census it had a population of 19,375.  The city is along the shore of Lake Michigan, and is a part of the Chicago metropolitan area and the North Shore.  Lake Forest was founded around Lake Forest College and was laid out as a town in 1857 as a stop for travelers making their way south to Chicago.  The Lake Forest City Hall, designed by Charles Sumner Frost, was completed in 1898 and originally housed the fire department, the Lake Forest Library, and city offices.  Lake Forest is among the wealthiest cities in the United States.

Frost &amp; Granger: Frost & Granger was an architectural partnership from 1898 to 1910 of brothers-in-law Charles Sumner Frost (1856–1931) and Alfred Hoyt Granger (1867–1939).  Frost and Granger were known for their designs of train stations and terminals, including the now-demolished Chicago and North Western Terminal, in Chicago.  The firm designed several residences in Hyde Park, Illinois, and many other buildings.  Several of their buildings are listed on the U.S. National Register of Historic Places.

Charles Sumner Frost: Charles Sumner Frost (May 31, 1856 – December 11, 1931) was an American architect.  He is best known as the architect of Navy Pier and for designing over 100 buildings for the Chicago and North Western Railway.

DuPage County Historical Museum: The DuPage County Historical Museum, formerly the Adams Memorial Library, is a building designed by Charles Sumner Frost in Wheaton, Illinois, United States.

Vernon Hills, Illinois: Vernon Hills is a village in Lake County, Illinois, United States, and an affluent northern suburb of Chicago.  The population was 20,120 at the 2000 census, and 25,113 in 2010.  Vernon Hills serves as a retail hub for its surrounding area (Libertyville, Mundelein, Lake Forest, Long Grove, Lincolnshire and Buffalo Grove).

Antigo Depot: The Antigo Depot is a historic railroad station in Antigo, Wisconsin.  The depot was designed in 1907 by Charles Sumner Frost of the architectural firm Frost & Granger in the Classical Revival style for the Chicago and North Western Railway.  The two-story building also housed offices for a Chicago and North Western division headquarters.  After rail service to the station ended, it was converted to apartments in 1992.  The depot was added to the National Register of Historic Places on February 10, 1992.

Palmer Mansion: The Palmer Mansion, constructed 1882–1885 at 1350 N. Lake Shore Drive, was once the largest private residence in Chicago, Illinois, located in the Near North Side neighborhood and facing Lake Michigan.  It was designed by architects Henry Ives Cobb and Charles Sumner Frost of the firm Cobb and Frost and built for Bertha and Potter Palmer.  Palmer was a prominent Chicago businessman who was responsible for much of the development of State Street.  The construction of the Palmer Mansion on Lake Shore Drive established the "Gold Coast" neighborhood, still one of the most affluent neighborhoods in the city.  The mansion was demolished in 1950.

Supporting paragraphs: Vernon Hills, Illinois Lake Forest, Illinois
Answer: 19,375