We have : \(AH^2=BH\cdot CH\Leftrightarrow3^2=BH\cdot6\Rightarrow BH=\dfrac{9}{6}=\dfrac{3}{2}\)

So \(BC=BH+CH=6+\dfrac{3}{2}=7,5\)

=> \(AC^2=7,5\cdot6\Rightarrow AC=3\sqrt{5}\)

So the area of the triangle ABC is 

\(S_{ABC}=\dfrac{1}{2}\cdot AB\cdot AC=\dfrac{1}{2}\cdot5\cdot3\sqrt{5}=\dfrac{15\sqrt{5}}{2}\)

The area of the triagle ABC is:

( 5 x 3 ) : 2 = 7,5 ( ....² )

Answer: 7,5 ....² 

Where is the unit Summer Clouds ?