Đáp án:
Gọi 2 cạnh của hình chữ nhật AB=CD=x; AD=BC=y
=> x.y=216
TA có:
$\begin{array}{l}
AE = \dfrac{2}{3}AB = \dfrac{2}{3}.x\\
BE = \dfrac{1}{3}AB = \dfrac{1}{3}.x\\
BF = \dfrac{2}{3}BC = \dfrac{2}{3}y\\
CF = \dfrac{1}{3}y\\
\Rightarrow \left\{ \begin{array}{l}
{S_{ADE}} = \dfrac{1}{2}.AD.AE = \dfrac{1}{2}.y.\dfrac{2}{3}x = \dfrac{1}{3}.x.y\\
{S_{BFE}} = \dfrac{1}{2}.BE.BF = \dfrac{1}{2}.\dfrac{1}{3}.x.\dfrac{2}{3}y = \dfrac{1}{9}x.y\\
{S_{DCF}} = \dfrac{1}{2}.DC.CF = \dfrac{1}{2}.x.\dfrac{1}{3}y = \dfrac{1}{6}xy
\end{array} \right.\\
\Rightarrow {S_{{\rm{DEF}}}} = {S_{ABCD}} - {S_{ADE}} - {S_{BFE}} - {S_{DCF}}\\
= x.y - \dfrac{1}{3}xy - \dfrac{1}{9}xy - \dfrac{1}{6}xy\\
= \dfrac{7}{{18}}xy\\
= \dfrac{7}{{18}}.216 = 84\left( {c{m^2}} \right)
\end{array}$
