The dispositive issue in this zoning appeal is whether the principles of equitable estoppel entitle the owners of a legally nonconforming building to a variance on the ground of hardship when, in reliance on an erroneously issued building permit, the owners have expanded and altered the building within the nonconforming areas. We conclude under the circumstances of this case that the property owners’ reliance on an erroneous building permit does not constitute such a hardship.
*200The following facts are undisputed. The defendants Kevin Conroy, Steven Cook and William Conroy (owners)1 are the owners of a restaurant located at 89 Rowayton Avenue in Norwalk. The property is zoned for business and a restaurant is a permitted use. The building that houses the restaurant, however, is nonconforming because part of the structure is within the thirty-five foot front setback included in the Norwalk zoning regulations.2 Because the building predates the present zoning regulations, it is a legally nonconforming structure that requires no modification.3
The owners decided to renovate the building and applied to the Norwalk zoning commission for approval. The proposed renovations included the construction of a dormer, which consists of a new raised roof with vertical windows, and the addition of a stoop. The proposed dormer was to be constructed above a nonconforming portion of the preexisting structure within the thirty-five foot setback. Also, the owners intended to add the stoop to a nonconforming portion of the building, slightly increasing the preexisting encroachment on the setback requirement. The owners did not provide the local zoning authorities with a map or survey indicating the front setback line.
On June 19,1991, the Norwalk zoning enforcement officer approved the project and certified that it complied with applicable zoning regulations. On July 17, 1991, the plan review committee of the Norwalk zon*201ing commission and the Norwalk zoning commission approved the project. The owners’ application was approved on July 31,1992, and a building permit was issued in August, 1992. Pursuant to these approvals, the owners began construction sometime in August or September, 1992.
In January, 1993, as a result of a complaint filed by the plaintiffs,4 the zoning enforcement officer issued a cease and desist order to the owners because the construction of the dormer and the stoop violated the thirty-five foot setback provision of the regulations. In response, on February 3, 1993, the owners applied to the defendant Norwalk zoning board of appeals (board) for a variance of fourteen feet for the dormer and 9.8 feet for the stoop. After a duly noticed public hearing, the board granted the owners’ application for the variance without making a specific finding regarding what hardship the owners would otherwise suffer. The plaintiffs appealed to the trial court.
On appeal, the trial court first concluded that the record failed to reflect any hardship that preexisted the construction that was commenced pursuant to the erroneously issued building permit. The court noted that a hardship is sufficient to justify a variance if it results from the peculiar topography, location or condition of the land that makes the property unsuitable for the use permitted in the zone. In this case, the trial court determined that the owners’ restaurant was a viable, ongoing concern before the construction began *202and that no hardship resulted from the characteristics of the property or the enforcement of the zoning regulations.
The trial court also rejected the owners’ argument that they were entitled to the variance under Lessner v. Zoning Board of Appeals, 151 Conn. 165, 195 A.2d 437 (1963), in which the court upheld a variance that was granted for construction that previously had been commenced pursuant to a zoning permit. The trial court distinguished Lessner by determining that the outcome in that case had turned on the fact that without the variance the defendant’s property would have been worthless and not on any finding that the defendant had obtained a zoning permit before undertaking construction.
Finally, the court noted that no case supports granting a variance because substantial construction had been undertaken based on the issuance of a building permit. Accordingly, the trial court determined that no traditional, legally cognizable hardship justified the variance. Ordinarily, as the trial court pointed out, this would have concluded its inquiry. Nevertheless, the trial court went on to conclude, in light of the principles of equitable estoppel, that the owners had demonstrated a hardship. On this basis, the court dismissed the plaintiffs’ appeal.
The plaintiffs appealed from the judgment of the trial court to the Appellate Court, and the appeal was transferred to this court pursuant to Practice Book § 4023 and General Statutes § 51-199 (c). The plaintiffs present the following claims on appeal, all of which pertain to the issue of equitable estoppel: (1) the trial court improperly determined that equitable estoppel gave rise to a hardship that justified the variance; (2) the trial court improperly imputed to the plaintiffs the conduct of the local zoning officials that was pertinent to the *203court’s estoppel analysis; (3) the trial court violated the plaintiffs’ due process rights by failing to hold a hearing on whether equitable estoppel applies to this appeal; and (4) even if the principles of equitable estoppel apply to variances, the requirements for its application were not satisfied in this case. The owners raise as alternate grounds for affirmance5 that the board properly granted the variance because the evidence submitted to the board was sufficient to establish that the owners had demonstrated a legally cognizable hardship. We agree with the trial court’s conclusion that there was no hardship according to the traditional analysis as it applies to variances. We conclude, however, that the trial court incorrectly dismissed the plaintiffs’ appeal on the ground that the variance was properly predicated on the principles of equitable estoppel. Accordingly, the judgment of the trial court cannot be sustained.
I
After rejecting any justification for the variance based on traditional grounds for hardship, the trial court stated that the owners “have another arrow in their quiver” and decided the appeal in their favor on the ground of equitable estoppel.6 The trouble with the *204trial court’s reasoning is that the arrow was not fashioned by the owners but by the trial court itself. The court, sua sponte, discussed at length the proposition that because the construction at issue had been induced by the acts of the zoning commission upon which the owners had justifiably relied, a hardship would result if the owners were now required to remove the improvements. The trial court concluded that the principles of equitable estoppel supported a finding of hardship and dismissed the plaintiffs’ appeal.
The theory of equitable estoppel had not been raised before the board. Furthermore, the owners had not raised it in the trial court, either in their response to the plaintiffs’ appeal, during the hearing in the trial court, or in their trial brief.7 Although the owners have been unable to cite to any case in which the doctrine of equitable estoppel was invoked successfully to support a variance,8 we have acknowledged that there are situations where the doctrine may be applicable to municipalities in the enforcement of the zoning laws. Dornfried v. October Twenty-Four, Inc., 230 Conn. 622, 634, 646 A.2d 772 (1994); Dupuis v. Submarine Base Credit Union, Inc., 170 Conn. 344, 354, 365 A.2d 1093 (1976). The doctrine requires, however, more than a mere act in reliance on the conduct of the municipality; see, e.g., Kimberly-Clark Corp. v. Dubno, 204 Conn. *205137, 149, 527 A.2d 679 (1987); and the factual issues that must be raised in order to support equitable estop-pel require an evidentiary hearing. Because the court held no evidentiary hearing on this subject, the plaintiffs never had an opportunity to present evidence to the trial court9 nor were they permitted the opportunity to present an argument on the legal applicability of the doctrine of equitable estoppel to justify a variance. A fundamental premise of due process is that a court cannot adjudicate any matter unless the parties have been given a reasonable opportunity to be heard on the issues involved; Sassone v. Lepore, 226 Conn. 773, 777, 629 A.2d 357 (1993); Costello v. Costello, 186 Conn. 773, 776-77, 443 A.2d 1282 (1982); and to present evidence and cross-examine adverse witnesses. Standard Tallow Corp. v. Jowdy, 190 Conn. 48, 56, 459 A.2d 503 (1983). Accordingly, the trial court incorrectly raised and decided the issue of whether the principles of equitable estoppel could support a hardship for the purposes of a variance.
II
We next turn to the alternate grounds for affirmance —the owners’ contention that they have established a legally cognizable hardship. The standard of review on appeal from a zoning board’s decision to grant or deny a variance is well established. We must determine whether the trial court correctly concluded that the *206board’s act was not arbitrary, illegal or an abuse of discretion. Schwartz v. Planning & Zoning Commission, 208 Conn. 146, 152, 543 A.2d 1339 (1988); Pike v. Zoning Board of Appeals, 31 Conn. App. 270, 624 A.2d 909 (1993). “Courts are not to substitute their judgment for that of the board . . . and decisions of local boards will not be disturbed so long as honest judgment has been reasonably and fairly exercised after a full hearing. . . . Upon appeal, the trial court reviews the record before the board to determine whether it has acted fairly or with proper motives or upon valid reasons. . . . We, in turn, review the action of the trial court. . . . The burden of proof to demonstrate that the board acted improperly is upon the plaintiffs.” (Citations omitted; internal quotation marks omitted.) Whit-taker v. Zoning Board of Appeals, 179 Conn. 650, 654, 427 A.2d 1346 (1980).
A variance constitutes permission to act in a manner that is otherwise prohibited under the zoning law of the town. Burlington v. Jencik, 168 Conn. 506, 508, 362 A.2d 1338 (1975). The Norwalk zoning regulations strictly limit the extent to which structural nonconfor-mities may be expanded or altered. Norwalk Zoning Regs. § 118-800. “A nonconforming structure shall not be enlarged or altered if the result would be an increase in the extent to which the structure does not conform to these regulations. A nonconforming structure may be enlarged or altered, provided that the enlargement or alteration conforms to these regulations.” Norwalk Zoning Regs. § 118-800 (D) (l).10
It is well established, however, that the granting of a variance must be reserved for unusual or exceptional *207circumstances. Dolan v. Zoning Board of Appeals, 156 Conn. 426, 429, 242 A.2d 713 (1968); Ward v. Zoning Board of Appeals, 153 Conn. 141, 145, 215 A.2d 104 (1965); Krejpcio v. Zoning Board of Appeals, 152 Conn. 657, 661-62, 211 A.2d 687 (1965); Kelly v. Zoning Board of Appeals, 21 Conn. App. 594, 598, 575 A.2d 249 (1990). “An applicant for a variance must show that, because of some peculiar characteristic of his property, the strict application of the zoning regulation produces an unusual hardship, as opposed to the general impact which the regulation has on other properties in the zone.” Dolan v. Zoning Board of Appeals, supra, 430. Accordingly, we have interpreted General Statutes (Rev. to 1993) § 8-611 to authorize a zoning board of appeals to grant a variance only when two basic requirements are satisfied: “(1) the variance must be shown not to affect substantially the comprehensive zoning plan, and (2) adherence to the strict letter of the zoning ordinance must be shown to cause unusual hardship unnecessary to the carrying out of the general purpose of the zoning plan.” (Internal quotation marks omitted.) Grillo v. Zoning Board of Appeals, 206 Conn. 362, 368, 537 A.2d 1030 (1988); Smith v. Zoning Board of Appeals, 174 Conn. 323, 326, 387 A.2d 542 (1978). Proof of exceptional difficulty or unusual hardship is *208absolutely necessary as a condition precedent to the granting of a zoning variance. Point O’Woods Assn., Inc. v. Zoning Board of Appeals, 178 Conn. 364, 368, 423 A.2d 90 (1979); Ward v. Zoning Board of Appeals, supra, 143; Kelly v. Zoning Board of Appeals, supra, 598. A mere economic hardship or a hardship that was self-created, however, is insufficient to justify a variance; Krejpcio v. Zoning Board of Appeals, supra, 662; and neither financial loss nor the potential for financial gain is the proper basis for granting a variance. Garibaldi v. Zoning Board of Appeals, 163 Conn. 235, 239, 303 A.2d 743 (1972).
In order to determine whether the board properly granted the subject variance, we must first consider whether the board gave reasons for its action. Scalzo v. Danbury, 224 Conn. 124, 129, 617 A.2d 440 (1992); Schwartz v. Planning & Zoning Commission, supra, 208 Conn. 152. “Where a zoning agency has stated its reasons for its actions, the court should determine only whether the assigned grounds are reasonably supported by the record and whether they are pertinent to the considerations which the authority was required to apply under the zoning regulations. . . . The [decision] must be sustained if even one of the stated reasons is sufficient to support it. . . . [This] applies where the agency has rendered a formal, official, collective statement of reasons for its action.” (Citations omitted; internal quotation marks omitted.) Protect Hamden/North Haven from Excessive Traffic & Pollution, Inc. v. Planning & Zoning Commission, 220 Conn. 527, 544, 600 A.2d 757 (1991). Where a zoning board of appeals does not formally state the reasons for its decision, however, the trial court must search the record for a basis for the board’s decision. Connecticut Resources Recovery Authority v. Planning & Zoning Commission, 225 Conn. 731, 743, 626 A.2d 705 (1993). In this case, although individual members of the board *209discussed reasons for granting the owners a variance, the board did not state a collective, official reason for its action.12 Accordingly, we must search the record as a whole to determine whether the evidence supports the board's decision to grant the variance. Id.
During the public hearing regarding the variance, evidence was presented that the zoning commission had granted the owners a permit to proceed with the construction of the dormer and the stoop, and that the owners had relied in good faith on the building permit when they commenced construction. It is apparent from the record that the only evidence of hardship that the owners presented to the board consisted of their reliance on an improperly granted building permit. We can reasonably conclude from the record that the board granted the variance because it determined that the owners had received approval for the improvements from the zoning commission and to require the removal of the dormer and the stoop would constitute a hardship.
In order to justify a variance, the hardship must differ from the conditions that generally affect the property owners in the same area and it must arise from circumstances beyond the control of the property owner seeking the variance. Smith v. Zoning Board of Appeals, supra, 174 Conn. 327. The hardship must originate in the regulation or ordinance and arise from the appli*210cation of the regulation or ordinance to the subject property. Pollard v. Zoning Board of Appeals, 186 Conn. 32, 39-40, 438 A.2d 1186 (1982); Whittaker v. Zoning Board of Appeals, supra, 179 Conn. 658. Financial considerations are relevant only if the application of the regulation or ordinance practically destroys the value of the property for any use to which it may be put and the regulation or ordinance as applied to the subject property bears little relationship to the purposes of the zoning plan. Grillo v. Zoning Board of Appeals, supra, 206 Conn. 369; Carlson v. Zoning Board of Appeals, 158 Conn. 86, 89-90, 255 A.2d 841 (1969).
In this case, the trial court found that the owners would not have been entitled to a variance before the improvements were made pursuant to the improperly granted building permit. We agree. The owners have shown only that their building is located on an irregularly shaped lot and “limitations imposed by the shape of the lot do not in themselves create a hardship . . . .” T. Tondro, Connecticut Land Use Regulation (2d Ed. 1993 Sup.) p. 29. Furthermore, there was no evidence that if the variance were denied the owners’ property would become worthless. On the contrary, as the trial court determined, the building housed a restaurant that was a viable business and a going concern.13
*211Therefore, the only existent hardship resulted exclusively from the owners’ reliance on the improperly granted building permit. We have never held that such an administrative error creates a legal hardship, and the owners are unable to point to any case extending the definition of hardship for the purposes of obtaining a variance to such circumstances. Cf. Wnuk v. Zoning Board of Appeals, 225 Conn. 691, 696-97, 626 A.2d 698 (1993) (arbitrary decision by zoning officer is insufficient basis for finding of hardship to grant variance). By arguing that reliance on an improperly granted building permit constitutes a legally cognizable hardship, the owners are merely attempting to bootstrap the principles of equitable estoppel onto the definition of a legally cognizable hardship. We have already rejected the application of equitable estoppel in this case because it was neither raised before the board nor raised before the trial court. Accordingly, we conclude that the trial court incorrectly determined that the owners were entitled to the variance.
The judgment is reversed and the case is remanded to the trial court with direction to sustain the plaintiffs’ appeal.
In this opinion the other justices concurred.
The trial court granted the owners’ motion to intervene as defendants.
The front setback is a zoning limitation that prohibits construction within thirty-five feet of the center line of the street. See Norwalk Zoning Regs., Schedule Limiting Height and Bulk of Buildings, Commercial and Industrial, Part 1 (1992).
Section 118-530 (C) (1) of the Norwalk zoning regulations provides in pertinent part: “The height, bulk, location and use of all buildings in existence at the time of adoption of this section are hereby declared to be in conformance with the requirements of this section . . . .”
The plaintiffs are Hillard Bloom, the estate of Norman Bloom, Willis Cavanagh, Peter Drummond-Hay, Bettina Drummond-Hay, Frank E. Raymond and Esther Raymond. The trial court found that Cavanagh and Drummond-Hay owned property within a radius of 100 feet from the land for which the variance was granted and that they were therefore aggrieved. General Statutes § 8-8 (1). The trial court went on to determine that “[s]ince some of the plaintiffs are aggrieved by the decision of the board, it is not necessary to resolve whether the other plaintiffs are aggrieved . . . .” (Internal quotation marks omitted.)
Practice Book § 4013 (a) (1) provides in pertinent part: “If any appellee wishes to (A) present for review alternate grounds upon which the judgment may be affirmed . . . that appellee shall file a preliminary statement of issues within fourteen days from the filing of the appellant’s preliminary statement of the issues.”
Equitable estoppel has been applied to municipalities in the enforcement of zoning laws to prevent the enforcement of zoning regulations under certain circumstances. Generally, estoppel requires that “the party against whom estoppel is claimed must do or say something calculated or intended to induce another party to believe that certain facts exist and to act on that belief; and the other party must change its position in reliance on those facts, thereby incurring some injury.” Dornfried v. October Twenty-Four, Inc., 230 Conn. 622, 635, 646 A.2d 772 (1994). “Although estoppel may not generally be invoked against a public agency in the exercise of its governmental functions . . . an exception is made where the party claiming *204estoppel would be subjected to a substantial loss if the municipality were permitted to negate the acts of its agents. . . . [Accordingly, we stated that estoppel] against municipalities is . . . limited and may be invoked against the enforcement of zoning regulations (1) only with great caution, (2) only when the resulting violation has been unjustifiably induced by an agent having authority in such matters, and (3) only when special circumstances make it highly inequitable or oppressive to enforce the regulations.” (Citations omitted; emphasis in original; internal quotation marks omitted.) Id.; see Dupuis v. Submarine Base Credit Union, Inc., 170 Conn. 344, 354, 365 A.2d 1093 (1976).
The transcript of the hearing in the trial court was not filed in this appeal.
The issue of whether the doctrine of equitable estoppel may be invoked to support a variance is not before us and we leave it for another day.
See General Statutes § 8-8 (k), which provides: “The court shall review the proceedings of the board and shall allow any party to introduce evidence in addition to the contents of the record if (1) the record does not contain a complete transcript of the entire proceedings before the board, including all evidence presented to it, pursuant to section 8-7a, or (2) it appears to the court that additional testimony is necessary for the equitable disposition of the appeal. The court may take the evidence or may appoint a referee or committee to take such evidence as it directs and report the same to the court, with his or its findings of facts and conclusions of law. Any report of a referee or committee shall constitute a part of the proceedings on which the determination of the court shall be made.”
The owners applied for a variance instead of appealing the cease and desist order, and have never argued that the construction of the dormer and stoop conformed to the regulations. Therefore, the board and the trial court considered the additions as increases in the extent to which the building did not conform to the regulations. We do the same.
General Statutes (Rev. to 1993) § 8-6 provides in pertinent part: “powers and duties of board of appeals. The zoning board of appeals shall have the following powers and duties ... (3) to determine and vary the application of the zoning bylaws, ordinances or regulations in harmony with their general purpose and intent and with due consideration for conserving the public health, safety, convenience, welfare and property values solely with respect to a parcel of land where, owing to conditions especially affecting such parcel but not affecting generally the district in which it is situated, a literal enforcement of such bylaws, ordinances or regulations would result in exceptional difficulty or unusual hardship so that substantial justice will be done and the public safety and welfare secured, provided that the zoning regulations may specify the extent to which uses shall not be permitted by variance in districts in which such uses are not otherwise allowed. . . .”
When the chairman of the zoning board of appeals moved to grant the variance, he stated: “Whereas the applicant has demonstrated [that] this is a legally non-conforming use at a twenty-five point two tenths setback where thirty-[five] feet is required. Whereas applicant proposes to provide a modest dormer addition to the North side of the property built upon the existing footprint and to provide a modest stoop at the South portion of the property with a suitable handrail for delivery of said supplies, and whereas a granting of [the] variance requested will not confer on the applicant any special privilege that is denied by this ordinance to other lands, buildings or structures in the same zoning district, I move for the granting of the variance. ...”
The owners rely on Stillman v. Zoning Board of Appeals, 25 Conn. App. 631, 596 A.2d 1, cert. denied, 220 Conn. 923, 598 A.2d 365 (1991), where a variance was granted for the construction of an additional encroachment on the setback in a legally nonconforming building. We do not consider Stillman dispositive in this case. In Stillman, there were permanent structures on an undersized but legally nonconforming lot that prevented the defendant from constructing the proposed addition at any location other than within the setback. Therefore, because construction was possible only within the setback, the court concluded that the defendant was entitled to a variance. Id., 636-37. In the case before us, the owners presented no evidence that the renovations could only be accomplished within the front setback. Furthermore, the fact that an owner is prohibited from adding new structures to the property does not constitute a legally cognizable hard*211ship. “If it is a hardship to not be able to use one's property as one wishes, then most setback variance applications would have to be granted.” T. Ton-dro, supra, pp. 29-30. Although we distinguish Stillman from this case, we do not necessarily endorse its holding.