The Usurpation of "America"

I was writing a letter to a friend in Nicaragua recently, and a random thought went through my head. Why does the United States have a monopoly on being referred to as "America?" The US, at 9158960 sq. km, is only 21% of the combined area of North and South America, and only contains 33% of the combined population. There are vast areas of land and throngs of people outside of the United States that are 'American,' but are never described as such. I realize that "United Statesian" is a bit of a mouthful, but we really are not doing the rest of the world justice by claiming to be the only true 'Americans.'