Consider a rectangular sheet of solid material of length \(\mathrm{ℓ}=9\mathrm{cm}\) and width \(\mathrm{d}=4\mathrm{cm}…

Consider a rectangular sheet of solid material of length \(\mathrm{ℓ}=9\mathrm{cm}\) and width \(\mathrm{d}=4\mathrm{cm}\). The coefficient of linear expansion is \(\alpha =3.1\times {10}^{-5}{\mathrm{K}}^{-1}\) at room temperature and one atmospheric pressure. The mass of sheet \(\mathrm{m}=0.1\mathrm{kg}\) and the specific heat capacity \({\mathrm{C}}_{\mathrm{v}}=900\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}\). If the amount of heat supplied to the material is \(8.1\times {10}^{2}\mathrm{J}\) then change in area of the rectangular sheet is :-

[JEE Main 2025, 4 Apr (Shift 2)]