What were a couple of things america was trying to gain in imperialism?

Idon’t have a clue on how i should understand this i’m in need of assistance.

What process is believed to be responsible for the formation of the grand canyon? a) diverging tectonic plates b) converging tectonic plates c) erosion over a long period of time d) caving in of the ground due to erosion

Idon’t understand 8. plz ! we are finding the area of polygons. thx in advance!