In a proceeding pursuant to CPLR *504article 78 to review a determination of the Board of Zoning and Appeals of the Town of North Hempstead dated March 14, 1988, denying the petitioners’ application for a variance, the appeal is from a judgment of the Supreme Court, Nassau County (Murphy, J.), entered September 20, 1988, which granted the petition and annulled the determination.
Ordered that the judgment is affirmed, without costs or disbursements.
The petitioners desired to subdivide an existing plot located on Shorecliff Place in Great Neck so that Lawrence Hofstein could build a house for his family adjacent to that of his mother. While the proposed subdivided plot far exceeded the minimum square footage for a buildable plot, it was approximately 20 inches short of the required 65 feet of frontage. Thus, the petitioners sought a variance of about 1.68 feet. The respondent Board of Zoning and Appeals of the Town of North Hempstead (hereinafter the Board) denied the application.
Although a zoning board is given discretion in determining whether or not to grant a variance, the Board’s determination must have a rational basis and be supported by substantial evidence (Matter of Consolidated Edison Co. v Hoffman, 43 NY2d 598). We agree with the Supreme Court’s finding that the Board’s denial of the petitioners’ application for an area variance in this case was arbitrary and capricious and constituted an abuse of discretion (see, Matter of Fuhst v Foley, 45 NY2d 441).
Strict application of the zoning regulations in this case will serve no valid public purpose outweighing the injury to the petitioners. The record demonstrates that the petitioners cannot build a dwelling on the property " 'without coming into conflict with certain [zoning restrictions]’ ”, and the restrictions would create " 'practical difficulties’ ” (Matter of Fuhst v Foley, supra, at 445, quoting from 3 Rathkopf, Law of Zoning and Planning, ch 45, § 1 [4th ed]; Matter of Townwide Props. v Zoning Bd. of Appeals, 143 AD2d 757; Matter of Lanzilotta & Teramo Dev. Corp. v Lazarus, 127 AD2d 767; Human Dev. Servs. v Zoning Bd. of Appeals, 110 AD2d 135, affd 67 NY2d 702). Not only is a variance of 20 inches with regard to a 65-foot frontage requirement de minimis (see, Matter of Townwide Props, v Zoning Bd. of Appeals, supra), the subdivided plot greatly exceeds all the other zoning requirements, including total square footage and side yard clearance. Moreover, without the variance, a plot capable of sustaining as many as three homes would be extremely underutilized to the detri*505ment of the petitioners without any corresponding benefit to the community. In fact, the record is devoid of any evidence that the proposed variance would have an adverse impact upon the surrounding area.
Accordingly, the Board’s denial of the application for a variance was arbitrary and capricious (Matter of Fuhst v Foley, supra; Matter of Townwide Props. v Zoning Bd. of Appeals, supra), and the Supreme Court properly annulled and vacated the Board’s determination. Lawrence, J. P., Rubin, Sullivan and Balletta, JJ., concur.