(a) The governing body of a municipality by ordinance may discontinue an area as a part of the municipality if:
(1) the municipality has a population of 4,000 or more and is located in a county with a population of more than 205,000, and the area is composed of at least three contiguous acres that are unimproved and adjoining the municipal boundaries; or
(2) the municipality has a population of 596,000 or more, and the area is an improved area that is not taxable by the municipality and is contiguous to the municipal boundary.
(b) On adoption of the ordinance, the governing body shall enter in the minutes or records of the municipality an order discontinuing the area. The area ceases to be a part of the municipality on the date of the entry of the order.