Costa Rica is part of the North American continent. Remember a continent is a geological term and not a political, cultural, nor lingual term. You don't end up in South America when you cross the border from San Diego to Tijuana or any other border crossings between the U.S. and Mexico. Panama divides North and South America since that is where the North American continent narrows down to a tiny ithmus. When you get to Columbia it widens and becomes South America. Central America is just the southern extreme of the North American Continent and isn't even a continent.
Freedomhammer got most of what is North America with one exception. He missed that a majority of Denmark is actually in North America since Greenland which is Danish territory is part of North America.
Of those that mentioned Mesoamerica, that is a cultural region of several related native civilazations(Maya, Aztec, Olmecs, Toltec, etc)that existed for about 3,000 years prior to the arrival of the Europeans. Mesoamerica is considered the area of Central Mexico to just north of Costa Rica.
Costa Rica WAS in Mexico. From January 1822 to July 1823 Costa Rica was part of Mexico but in July 1823 it became a province in the United Provinces of Central America. It then became an independent nation after a civil war between 1838-1840 which dissolved the union.
Meme D also depends on where you are from. Some countries such as the United States consider there to be 7 continents. Others believe there are 6. For example sometimes Europe and Asia are considered to be one giant continent.