[tex]\displaystyle\bf\\\triangle ABC\sim\triangle ADE\\\\BC=15~cm\\\\DE=10~cm\\\\Raportul~de~asemanare~dintre~\triangle ABC~si~\triangle ADE~este:\\\\k=\frac{BC}{DE}=\frac{15}{10}=1,\!5\\\\\implies~Raportul~ariilor=k^2=1,\!5^2=\boxed{\bf2,\!25}\\\\\implies aria~\triangle ADE~\textbf{ este de 2,25 ori mai mica decat aria }\triangle ABC.\\\\Aria~\triangle ABC=90~cm^2\\\\Aria~\triangle ADE=\frac{Aria~\triangle ABC}{2,25}=\frac{90~cm^2}{2,25}= \boxed{\bf40~cm^2}[/tex]
