\(SA\perp\left(ABC\right)\Rightarrow SA\perp BC\)
Mà \(BC\perp AB\Rightarrow BC\perp\left(SAB\right)\Rightarrow BC\perp SB\Rightarrow\Delta SBC\) vuông tại B
\(AC=\sqrt{AB^2+BC^2}=a\sqrt{2}\) ;\(SB=\sqrt{SA^2+AB^2}=a\sqrt{2}\)
\(S_{tp}=S_{SAC}+S_{SAB}+S_{SBC}+S_{ABC}\)
\(S_{tp}=\frac{1}{2}\left(SA.AC+SA.AB+SB.BC+AB.BC\right)\)
\(S_{tp}=\frac{1}{2}\left(a^2\sqrt{2}+a^2+a^2\sqrt{2}+a^2\right)=\left(\sqrt{2}+1\right)a^2\)