For the purpose of promoting the health, safety, and general welfare of the community, the city council in a city of the metropolitan class may regulate and restrict the height, number of stories, and size of buildings and other structures, the percentage of a lot that may be occupied, the size of yards, courts, and other open spaces, the density of population, and the location and use of buildings, structures, and land for trade, industry, residence, or other purposes. Such regulations may provide for a board of appeals that may determine and vary application of such regulations in harmony with their general purpose and intent, and in accordance with general or specific rules contained in such regulations.