Răspuns:
Fie [tex]AB=L, \ AD=l, \ A_{ABCD}=S=L\cdot l[/tex]. Atunci
[tex]A_{EDF}=\displaystyle\frac{\frac{L}{2}\cdot\frac{l}{2}}{2}=\frac{L\cdot l}{8}=\frac{S}{8}[/tex]
[tex]A_{EFB}=\displaystyle\frac{L\cdot\frac{l}{2}}{2}=\frac{L\cdot l}{4}=\frac{S}{4}[/tex]
[tex]A_{FCB}{=\displaystyle\frac{\frac{L}{2}\cdot l}{2}=\frac{L\cdot l}{4}=\frac{S}{4}[/tex]
Atunci
[tex]A_{BEF}=S-\displaystyle\frac{S}{8}-\frac{S}{4}-\frac{S}{4}=\frac{3S}{8}\Rightarrow\frac{A_{BEF}}{A_{ABCD}}=\frac{\frac{3S}{8}}{S}=\frac{3}{8}[/tex]
Deci răspunsul este c).
Explicație pas cu pas:
