a,
$S_{ABC}=\dfrac12×15×10=75cm^2$
Vì $M$ là trung điểm $BC$
$→S_{ABM}=S_{MAC}$
$→S_{ABM}=\dfrac12×S_{ABC}=37,5cm^2$
$S_{MAC}=37,5cm^2$
Vì $DC=\dfrac13 AC$
$→S_{BDC}=\dfrac13×S_{ABC}=25cm^2$
b,
$DC=\dfrac13 AC$
$→AD=\dfrac23 AC$
$→S_{ABD}=\dfrac23×S_{ABC}=50cm^2$
$S_{BDC}=S_{ABC}-S_{ABD}=25cm^2$
$M$ là trung điểm $BC$ mà:
$BI$ song song $BM$
$DI$ song song $MC$
$→BI=DI$
$→S_{ABI}=S_{AID}$
Do $S_{ABI}=S_{AID}$ mà $S_{ABD}=50cm^2$
$→S_{ABI}=S_{AID}=25cm^2$
$→S_{IMCD}=S_{MAC}-S_{AID}=12,5cm^2$
