Question

Multumesc frumos!!!!

Answer 1

   
$\text{Suprafata evidentiata este patrulaterul concav DFME.} \\ A_{DFME} = A_{\boxed{}ABCD} -A_{\boxed{}MFBE}-A_{\Delta DAF} -A_{\Delta DEC}= \\ \\ =(x+3x)^2-(3x)^2- \frac{x(x+3x)}{2}- \frac{x(x+3x)}{2}= \\ \\ =16 x^{2} -9 x^{2} - \frac{4x^2}{2}- \frac{4x^2}{2}= \\ \\ 16 x^{2} -9 x^{2} -2x^2-2x^2= x^{2}(16-9-2-2)=\boxed{3 x^{2} }$

Answer 2

$FD-diagonala~dreptunghiului~AFHD \Rightarrow A_{AFD}= \frac{A_{AFHD}}{2}. \\ \\ ED-diagonala~dreptunghiului~CEGD \Rightarrow A_{CED}= \frac{A_{CEGD}}{2}. \\ \\ A_{AFD}= \frac{A_{AFHD}}{2}= \frac{AF \cdot FH}{2}= \frac{x \cdot 4x}{2}=2x^2. \\ \\ A_{CED}= \frac{A_{CEGD}}{2}= \frac{GD \cdot CD }{2}= \frac{x \cdot 4x}{2}=2x^2. \\ \\ A_{hasurata}=A_{AFHD}+A_{CEGD}-A_{GDHM}-A_{AFD}- A_{CED}= \\ \\ =4x^2+4x^2-x^2-2x^2-2x^2= \\ \\ = \boxed{3x^2}$