Kẻ MH ⊥ BC, EK ⊥ BC.

Ta có: (g.g)

\( \Rightarrow \frac{{ME}}{{MB}} = \frac{{B'E}}{{CB}} = \frac{1}{2}\).

(g.g)

\( \Rightarrow \frac{{MH}}{{KE}} = \frac{{BM}}{{BE}} = \frac{2}{3}\)

\( \Rightarrow MH = \frac{2}{3}EK = \frac{2}{3}.6a = 4a\)

\(V = \frac{1}{3}MH.{S_{\Delta ABC}} = \frac{1}{3}.4a.\left( {\frac{1}{2}.3a.3a} \right) = 6{a^3}\).