The City of Sunshine is in the process of bringing a hockey team to the area and will need land on which to build a new arena. The site has been selected and Sunshine officials have offered the homeowners a fair amount for the property where the arena is to be built. What would this action fall under?

This action would fall under the Fifth Amendment's eminent domain.

Explanation:

Eminent domain is the legal term used to denote the deprivation of ownership of an immovable or movable property by the state, within the framework of the law and against compensation. An overriding purpose serving the common good is cited as the justification for expropriations for traffic, military and other reasons related to state tasks.  

Since property is one of the basic rights in market-based democracies, expropriations are only possible there in certain legally regulated exceptional cases. Thus, in America this is reflected in the Fifth Amendment, which establishes that property can only be expropriated for public use and with due compensation.

your answer would be a. true