To address the distortion issues of the thin plate deformation reconstruction, this study developed a quadrilateral element model based on the area coordinate shape function. Unlike the traditional isoparametric transformation method reliant on the Jacobian matrix, this approach introduces area coordinates as an intermediary between isoparametric and Cartesian coordinates. This ensures linear conversion and second-order completeness of shape functions, eliminating precision degradation caused by element distortion in isoparametric transformations and enhancing the model′s adaptability for complex structures. Considering the practical limitations of sensor placement, the study also presents a reconstruction method based on single-surface strain, grounded in the first-order shear deformation theory of classical Kirchhoff plates. By developing a multi-objective particle swarm optimization model, the optimal sensor layout for single-surface arrangement was determined. Simulation and experimental validation on an antenna structure model demonstrated that with a maximum deformation of 60 mm, the root mean square error (RMSE) was 0.72 mm, and the percentage error (PD) was 2.89%. This method achieved high-precision deformation reconstruction of antenna structures and shows promise for application in the design and manufacturing of deformable antenna structures.