In order to determine all the public (non-private) floodplain areas you were responsible for maintaining, the right way to go about it is to use a spatial intersection analysis.
What is spatial intersection analysis?
Firstly, it will help you to note that a floodplain, also known as a flood plain or bottomlands, is a piece of land close to a river.
Secondly, note that spatial intersection analysis can be likened to the use of a magnifying glass to see where different shapes overlap on a map.
One way to look at this is to imagine a floodplain or a private property and checking to analyze all the areas where the shapes of these areas meet.
In simpler terms, spatial intersection analysis helps a person determine which parts of a flood plain fall within an area. This way they can assess the risk of that area being flooded so they can plan in advance.