The terms of members of the board shall be four years, except that members of the initial board shall determine their respective terms by lot so that the terms of one-half of the members, as nearly as may be, shall expire at the next general election. The remaining initial terms shall expire at the following general election. The successors of the initial board shall be chosen from area districts at regular elections, and shall be nominated and elected in the same manner as county hospital trustees as provided in section 347.25, except that nomination papers on behalf of a candidate shall be signed by not less than twenty-five eligible electors from the area district.