Ta có: \(\left\{ \begin{array}{l}BC \bot AB\\BC \bot AA'\end{array} \right. \Rightarrow BC \bot \left( {A'BA} \right) \Rightarrow \widehat {A'BA} = 30^\circ \)

Khi đó \(AA' = AB.\tan 30^\circ = \frac{{2a}}{{\sqrt 3 }}\)

\( \Rightarrow {V_{ABC.A'B'C'}} = {S_{ABC}}.AA' = \frac{{4{a^2}}}{2}.\frac{{2a}}{{\sqrt 3 }} = \frac{{4{a^3}\sqrt 3 }}{3}\)