Đáp án:
$\begin{array}{l}
Theo\,Pytago:\\
B{D^2} = A{D^2} + A{B^2} = 100\\
\Rightarrow BD = 10\left( {cm} \right)\\
\Delta DAH \sim \Delta DBA\left( {g - g} \right)\\
\Rightarrow \dfrac{{AD}}{{BD}} = \dfrac{{AH}}{{AB}} = \dfrac{{DH}}{{AD}}\\
\Rightarrow \left\{ \begin{array}{l}
AH = \dfrac{6}{{10}}.8 = 4,8\left( {cm} \right)\\
DH = \dfrac{6}{{10}}.6 = 3,6\left( {cm} \right)
\end{array} \right.\\
\Rightarrow BH = BD - DH = 10 - 3,6 = 6,4\left( {cm} \right)\\
\Rightarrow \dfrac{{BH}}{{BD}} = \dfrac{{6,4}}{{10}} = \dfrac{{16}}{{25}}\\
\Rightarrow \dfrac{{{S_{CHB}}}}{{{S_{CDB}}}} = \dfrac{{BH}}{{BD}} = \dfrac{{16}}{{25}}\\
\Rightarrow {S_{CHB}} = \dfrac{{16}}{{25}}.\dfrac{1}{2}.BC.CD = \dfrac{{384}}{{25}}\left( {c{m^2}} \right)\\
{S_{AHB}} = \dfrac{1}{2}.AH.BH = \dfrac{1}{2}.4,8.6,4 = \dfrac{{384}}{{25}}\left( {c{m^2}} \right)\\
\Rightarrow {S_{AHCB}} = {S_{CHB}} + {S_{AHB}} = \dfrac{{768}}{{25}}\left( {c{m^2}} \right) = 30,72\left( {c{m^2}} \right)
\end{array}$
