Draw \(CK\perp AB\)

\(\widehat{CBK}=180^0-\widehat{ABC}=180^0-\dfrac{180^0\left(8-2\right)}{8}=45^0\)

\(\Rightarrow CK=\dfrac{BC}{\sqrt{2}}=\sqrt{2}\)

\(S_{ABC}=\dfrac{AB.CK}{2}=\dfrac{2\sqrt{2}}{2}=\sqrt{2}\left(cm^2\right)\)