\(BH=\frac{AB.AC}{BC}=\frac{3.4}{5}=\frac{12}{5}=2,4\)
Trung tuyến ứng với cạnh huyền bằng nửa cạnh huyền => MC = 2,5
\(S_{BMC}=\frac{1}{2}MC.BH=3\left(cm^2\right)\)
\(AH=\frac{AB^2}{AC}=\frac{9}{5}=1,8\left(cm\right)\)
\(S_{ABH}=\frac{1}{2}AH.BH=2,16\left(cm^2\right)\)
BK là TPG
\(\frac{AK}{AB}=\frac{KC}{BC}=\frac{AK+KC}{AB+BC}=\frac{5}{7}\)
\(KC=\frac{20}{7}\left(cm\right)\)
\(KM=KC-MC=\frac{20}{7}-2,5=\frac{5}{14}\)
\(S_{BKM}=\frac{1}{2}BH.KM=\frac{3}{7}\)
\(S_{BHK}=S_{ABC}-S_{BKM}-S_{BMC}-S_{BHA}=\frac{72}{175}\)