Đáp án:
$S_{AOB}= 182\ cm^2$
Giải thích các bước giải:
Ta có: $AD//BC\quad (gt)$
$\Rightarrow \triangle AOD\backsim \triangle COB$
$\Rightarrow \dfrac{S_{AOD}}{S_{COB}}=\left(\dfrac{OD}{OB}\right)^2$
$\Rightarrow \dfrac{196}{169}= \left(\dfrac{OD}{OB}\right)^2$
$\Rightarrow \dfrac{OD}{OB}=\dfrac{14}{13}$
$\Rightarrow \dfrac{S_{AOD}}{S_{AOB}}=\dfrac{14}{13}$
$\Rightarrow S_{AOB}=\dfrac{13}{14}S_{AOD}$
$\Rightarrow S_{AOB}=\dfrac{13}{14}\cdot 196 = 182\ cm^2$
Vậy $S_{AOB}= 182\ cm^2$