Áp dụng hệ thức lượng :
\(\frac{1}{AH^2}=\frac{1}{AB^2}+\frac{1}{AC^2}\)
\(\Leftrightarrow\frac{1}{12^2}=\frac{1}{AB^2}+\frac{1}{20^2}\)
\(\Leftrightarrow\frac{1}{AB^2}=\frac{1}{225}\)
\(\Leftrightarrow AB=15cm\)
\(\Leftrightarrow S_{ABC}=\frac{AB.AC}{2}=\frac{20.15}{2}=150cm^2\)