Final answer:
The Gadsden Purchase, a diplomatic action, added territory to the United States between 1840 and 1855.
Step-by-step explanation:
One diplomatic action that added territory to the United States in the period 1840 to 1855 was the Gadsden Purchase. The Gadsden Purchase was a treaty signed between the United States and Mexico in 1854, during the presidency of Franklin Pierce. It resulted in the acquisition of a strip of land in present-day Arizona and New Mexico, which was purchased for $10 million. This territory was obtained to facilitate the construction of a southern transcontinental railroad route and secure U.S. interests in the region.