\(\left\{{}\begin{matrix}BO\cap\left(SAD\right)=D\\BD=2OD\end{matrix}\right.\) \(\Rightarrow d\left(B;\left(SAD\right)\right)=2d\left(O;\left(SAD\right)\right)\)
Gọi M là trung điểm AD \(\Rightarrow OM\perp AD\Rightarrow AD\perp\left(SOM\right)\)
Trong mp (SOM), từ O kẻ \(OH\perp SM\Rightarrow OH\perp\left(SAD\right)\Rightarrow OH=d\left(O;\left(SAD\right)\right)\)
\(OD=\dfrac{1}{2}\sqrt{BC^2+CD^2}=\dfrac{a\sqrt{2}}{2}\Rightarrow SO^2=SD^2-OD^2=16a^2\)
\(OM=\dfrac{1}{2}AB=\dfrac{a}{2}\)
Áp dụng hệ thức lượng: \(\dfrac{1}{OH^2}=\dfrac{1}{SO^2}+\dfrac{1}{OM^2}=\dfrac{1}{16a^2}+\dfrac{4}{a^2}=\dfrac{65a^2}{16}\)
\(\Rightarrow OH=\dfrac{4a\sqrt{65}}{65}\Rightarrow d\left(B;\left(SAD\right)\right)=\dfrac{8a\sqrt{65}}{65}\)
