—In a proceeding pursuant to CPLR article 78 to review a determination of the Zoning Board of Appeals of the Town of Shelter Island dated September 28, 1982, granting Kenneth and Donna L. Wright’s application for a variance, petitioners appeal (1) from an order of the Supreme Court, Suffolk County (D’Amaro, J.), dated June 14, 1984, which dismissed the proceeding on the merits, and a judgment of the same court, dated July 10, 1984, entered thereon.
Appeal from the order dismissed, without costs or disbursements (see, CPLR 5701 [b] [1]; Matter of Aho, 39 NY2d 241, 248).
Judgment reversed, on the law, without costs or disbursements, order vacated, and petition granted to the extent that the determination is annulled, and the Wrights’ application for a variance is denied.
Kenneth and Donna Wright are the owners of a parcel of land approximately 200 feet long and 50 feet wide, located on Shelter Island. This narrow strip of land provides the Wrights with access to West Neck Harbor. There is a dock located at the edge of the property, which extends into the harbor.
The Wrights sought permission to build a small shed on this property. The Building Inspector of the Town of Shelter Island denied this request, and notified the Wrights by letter dated September 10, 1982, that (1) no accessory building could be constructed on the property in the absence of a principal building, and (2) the proposed accessory building did not conform to the applicable set-back requirements. The Wrights appealed to the Zoning Board of Appeals, and requested a variance. The board, after a hearing at which local residents voiced opposition to the proposal, approved the variance. The instant proceeding was commenced by various local residents. Special Term dismissed the proceeding, and this appeal followed. We reverse.
The determination of the Zoning Board of Appeals to ap*607prove a use variance is arbitrary and lacks a rational basis. Under the Shelter Island Zoning Code, an accessory building is permitted as of right in a District A (Residential) Zone only if there is a principal building located on the same parcel (Shelter Island Zoning Code § 133-5 [c] [2]). It is absolutely clear that the proposed structure, a shed approximately 12 feet by 15 feet in size is an accessory, not a principal, building, and it is undisputed that no principal building is located on the subject property. In order to be entitled to a use variance, the applicant would have to establish, among other things, economic hardship, and such hardship must be shown by "dollars and cents” proof (see, Matter of Village Bd. v Jarrold, 53 NY2d 254; Matter of Commco v Amelkin, 109 AD2d 794). There is no proof of such hardship in this case, nor is there any proof of the other criteria necessary to establish the right to a use variance (see, Matter of Otto v Steinhilber, 282 NY 71, 76, reh denied 282 NY 681). The most that the Wrights proved is that the shed that they proposed to build, which would be used for the storage of sailing equipment, would relieve them of the inconvenience of having to store sailboat equipment at their nearby home, which is farther from the water, on another parcel of land. This falls far short of the showing one must make in order to establish a right to a use variance. The record, therefore, does not contain substantial evidence to support the determination of the Zoning Board of Appeals.
Special Term, nevertheless, confirmed the zoning board’s erroneous determination on the basis of an argument which had not been raised during the administrative proceedings, namely, that the proposed shed, in conjunction with the existing dock, constitutes a "marina”, which is permitted as of right (Shelter Island Zoning Code § 133-5 [c] [3]). We consider the application of the term "marina” to a solitary private dock to be, as a matter of ordinary English usage, erroneous. Accordingly, we reverse, and annul the determination under review. Gibbons, J. P., Thompson, Niehoff and Kunzeman, JJ., concur.