a) Ta có: \(AH=\dfrac{2}{3}.BC=\dfrac{2}{3}.12=8\) \((\text{cm})\).
Diện tích tam giác \(ABC\) là: \(\dfrac{1}{2}AH.BC=\dfrac{1}{2}.8.12=48\) \((\text{cm}^2)\).
b) Ta có: \(CM=\dfrac{3}{5}BM\Rightarrow CM=\dfrac{3}{8}.BC=\dfrac{3}{8}.12=\dfrac{9}{2}\) \((\text{cm})\).
Diện tích tam giác \(ACM\) là: \(\dfrac{1}{2}.AH.CM=\dfrac{1}{2}.8.\dfrac{9}{2}=18\) \((\text{cm}^2)\).