To hear and decide appeals where it is alleged there is an error in any order, requirement, decision, or determination made by an administrative official in the enforcement of this ordinance.

When a property owner can show that a strict application of the terms of this ordinance relating to the use, construction or alteration of buildings or structures or the use of land will impose upon him practical difficulties or particular hardship, the board may consider and allow variations of the strict application of the terms of this ordinance if the variations are in harmony with the general purpose and intent of this ordinance, and the board is satisfied, under the evidence heard by it, that a granting of the variation will not merely serve as a convenience to the applicant but will alleviate some demonstrable hardship or difficulty so great as to warrant a variation from the comprehensive plan by this ordinance created.

The board may authorize a variance where, by reason of exceptional narrowness, shallowness or shape of a specific piece of property of record at the time of the adoption of this ordinance or by reason of exceptional topographical conditions or other extraordinary or exceptional situation or condition of a specific piece of property, the strict application of a provision of this ordinance would result in peculiar and exceptional practical difficulties and particular hardship upon the owner of the property and amount to a practical confiscation of the property as distinguished from a mere inconvenience to the owner, provided the variation can be granted without substantial detriment to the public good and without substantially impairing the general purpose and intent of the comprehensive plan as established by the regulations and provisions contained in this ordinance.