Final answer:
The Treaty of Guadalupe Hidalgo and the Gadsden Purchase increased the area of the United States by one-third.
Step-by-step explanation:
The Treaty of Guadalupe Hidalgo and the Gadsden Purchase significantly expanded the territory of the United States. Through the treaty, which ended the Mexican-American War, and the subsequent land purchase, the United States acquired a vast territory that eventually became part or all of several states including California, Arizona, New Mexico, Texas, Utah, Nevada, Colorado, Wyoming, and Kansas. This expansion contributed greatly to the concept of Manifest Destiny, as the nation grew territoriality.
In terms of land area, Mexico ceded approximately 525,000 square miles to the United States as a result of the Treaty of Guadalupe Hidalgo, which represented more than half of its territorial land mass at the time. This land cession, coupled with the additional territory acquired through the Gadsden Purchase, increased the land area of the United States significantly. To quantify this, we can approximate based on the approximate total area of the U.S. before these acquisitions to assess that it increased by about one-third.
Considering the totality of the land ceded by Mexico and then acquired through the Gadsden Purchase, the correct answer to the student's question is that the Treaty of Guadalupe Hidalgo and the Gadsden Purchase increased the area of the United States by one-third.