Any improvement district created by a district may embrace two or more separate property areas. Each improvement district must be of such size and form as to include all properties which in the judgment of the board, after consultation with the engineer planning the improvement, will be benefited by the construction of the improvement project which is proposed to be made in or for the district, or by any portion of the project. A single district may be created for an improvement of the type specified in section 61-35-48, notwithstanding any lack of uniformity among the types, items, or quantities of work and materials to be used at particular locations throughout the improvement district. The jurisdiction of a district to make, finance, and assess the cost of any improvement project may not be impaired by any lack of commonness, unity, or singleness of the location, purpose, or character of the improvement, or by the fact that any one or more of the properties included in the improvement district is subsequently determined not to be benefited by the improvement, or by a particular portion of the improvement project, and is not assessed for that purpose. The board may omit from a water or sewer district properties within the district limits which are benefited by the improvement but do not abut upon a water or sewer main, without prejudice to the right and power of the district subsequently to assess such properties to the extent and the manner permitted by law. The board may by resolution enlarge an improvement district in which an improvement is proposed or under construction upon receipt of a petition signed by the owners of three-fourths of the area to be added to the district.