\(AP=2PB\Leftrightarrow AP+2AP=2\left(PB+AP\right)\Leftrightarrow AP=\frac{2}{3}AB\)
\(AQ=3QC\Leftrightarrow AQ+3AQ=3\left(QC+AQ\right)\Leftrightarrow AQ=\frac{3}{4}AC\)
\(S_{APC}=\frac{2}{3}S_{ABC}\)(chung đường cao hạ từ \(C\), \(AP=\frac{2}{3}AB\))
\(S_{APQ}=\frac{3}{4}S_{APC}=\frac{3}{4}\times\frac{2}{3}S_{ABC}=\frac{1}{2}S_{ABC}\)(chung đường cao hạ từ \(B\), \(AQ=\frac{3}{4}AC\))
\(S_{PQCB}=S_{ABC}-S_{APQ}=S_{ABC}-\frac{1}{2}S_{ABC}=\frac{1}{2}S_{ABC}\)
\(\Leftrightarrow S_{ABC}=2S_{PQCB}=2\times180=360\left(cm^2\right)\)
