Răspuns :
Fie EF⊥AB
[tex]A_{EAB}=18cm^2\\\\\frac{EF\times AB}{2} =18\\\\EF\times 8=36\\\\EF=\frac{9}{2} =4,5cm[/tex]
AB=8 cm
CD=2 cm
Fie EM⊥CD
- Stim ca Aria a doua triunghiuri asemenea este egala cu patratul raportului de asemanare.
DC║AB⇒ ΔCED~ΔAEB
[tex]\frac{CE}{EA} =\frac{DE}{EB} =\frac{CD}{AB}=k \\\\\frac{CD}{AB}=k\\\\k=\frac{2}{8} =\frac{1}{4}[/tex]
[tex]\frac{A_{CED}}{A_{AEB}} =(\frac{1}{4})^2 \\\\\frac{A_{CED}}{A_{AEB}}=\frac{1}{16} \\\\\frac{A_{CED}}{18}=\frac{1}{16}\\\\A_{CED}=\frac{9}{8} =\frac{EM\times CD}{2} \\\\EM\times 2=\frac{18}{8} \\\\EM=\frac{9}{8}[/tex]
[tex]MF=EM+EF=\frac{9}{8}+\frac{9}{2} =\frac{45}{8} \\\\\\A_{ABCD}=\frac{(CD+AB)\times MF}{2} =\frac{10\times \frac{45}{8} }{2} =\frac{450}{16} =\frac{225}{8} cm^2[/tex]
