Hear and decide appeals where it is alleged that there is error in any order, requirement, decision or determination made by the Administrator.

Grant variances in the regulations when a property owner can show that his property was acquired in good faith and, where by reason of the exceptional narrowness, shallowness or shape of a specific piece of property at the time of the effective date of the chapter or where by reason of the exceptional topographical conditions or other extraordinary or exceptional situation, the strict application of the terms of this chapter would actually prohibit or unreasonably restrict the use of the property; or where the Board is satisfied, upon the evidence heard by it, that the granting of such variation will alleviate a clearly demonstrable hardship approaching confiscation as distinguished from a special privilege or convenience sought by the owner.