Final answer:
The Treaty of Guadalupe Hidalgo and the Gadsden Purchase expanded the U.S. by 525,000 square miles and approximately 30,000 acres, respectively, furthering the concept of Manifest Destiny.
Step-by-step explanation:
The Treaty of Guadalupe Hidalgo and the Gadsden Purchase significantly increased the area of the United States. The Treaty of Guadalupe Hidalgo, signed in February 1848 after the Mexican-American War, resulted in the United States acquiring a vast expanse of territory that included the present-day states of California, Arizona, New Mexico, Texas, Utah, Nevada, and parts of Colorado and Wyoming, amounting to approximately 525,000 square miles.
In addition, the Gadsden Purchase in 1853 added around 30,000 acres to the U.S. territory by acquiring land from Mexico for $10 million, which became southern Arizona and a portion of southern New Mexico, further shaping the southern boundary of the United States.
This expansion was driven by the ideology of Manifest Destiny, a belief that the expansion of the U.S. across the American continents was both justified and inevitable. It also set the stage for additional conflict and displacement of indigenous peoples and Mexican citizens residing in these regions.