Cho hình chóp S.ABCD có đáy là hình vuông cạnh a căn 3

* Hướng dẫn giải

Chọn B.

$$\begin{gathered} \left\{\begin{array}{l}AB//CD\\ AB\not\subset \left(SCD\right)\end{array}\right.\Rightarrow AB//\left(SCD\right). \\ \left\{\begin{array}{l}\left(SCD\right)\perp \left(SAD\right)\\ \left(SCD\right)\cap \left(SAD\right)=SD\end{array}\right. kẻ AH\perp SD=\left\{H\right\}\Rightarrow d\left(B,\left(SCD\right)\right)=d\left(A,\left(SCD\right)\right)=AH. \\ SD=\sqrt{S{A}^2+A{D}^2}=\sqrt{{\left(a\sqrt{2}\right)}^2+{\left(a\sqrt{3}\right)}^2}=a\sqrt{5}. \\ \Delta SAD\perp A:AH.SD=SA.AD\iff AH=\frac{SA.AD}{SD}=\frac{a\sqrt{2}.a\sqrt{3}}{a\sqrt{5}}=\frac{a\sqrt{30}}{5} \end{gathered}$$