(A)   Variances from standards. In any case where, upon application of any subdivider to the Board of Adjustment, it appears by reason of exceptional circumstances, that the strict enforcement of any provision of the standards would cause unusual hardship under the circumstances, the Board of Adjustment may permit a variance therefrom upon such conditions as it may prescribe consistent with the general purposes of this chapter and the intent of this and all other applicable State and local regulation.
   (B)   Appeals. The Board of Adjustment shall hear and decide appeals from and review any order, requirements, decisions or determinations made by any city Administrative Officer charged with enforcing any provision of this chapter.