2. In an acute triangle $ABC$, $AD$, $DE$, $CF$ are altitudes, $H$ is the orthocenter of the triangle. If $EF$ bisects the area of triangle $ABC$, then $DE^2 + EF^2 + FD^2 =$ $\qquad$ (Given the side lengths of the triangle are $3$, $2\sqrt{2}$, $\sqrt{5}$)