Final answer:
After the war with Mexico, the United States gained significant territory in the American Southwest through the Treaty of Guadalupe Hidalgo.
Step-by-step explanation:
In the aftermath of the war with Mexico, the United States gained large amounts of territory in the American Southwest. This territorial acquisition was a result of the Treaty of Guadalupe Hidalgo, which ended the Mexican-American War in 1848. The treaty transferred the territories of Alta California and New Mexico to the United States, amounting to some 525,000 square miles. Subsequently, the land ceded by Mexico eventually formed all or parts of states including California, Arizona, New Mexico, Texas, Utah, Nevada, Colorado, Wyoming, and Kansas. As a result of this treaty, Mexico lost more than half of its total land area to the expanding United States.