No building or premises shall be used, and no building shall be erected or altered except in conformity with the regulations prescribed for the zone in which such buildings or premises are located. Where a lot is formed from part of a lot already occupied by a building, such subdivision shall be effected in such a manner as not to impair any of the requirements of this chapter with respect to the existing building and all yards and other open space in connection therewith and so that all resulting lots have adequate dimensions consistent with the requirements of the zoning district in which they are located and so that all lots have frontage.