Question

Arii.
M este un punct in interiorul dreptunghiului ABCD. Demonstrati ca S[MAB]+S[MCD]=S[MAD]+S[MBC].

Answer 1

[tex]S_{MAB}+S_{MCD}=\dfrac{AB}{2}\cdot h_1+ \dfrac{BC}{2}\cdot h_2=\dfrac{AB}{2}\cdot h_1+ \dfrac{AB}{2}\cdot h_2\\ S_{MAB}+S_{MCD}=\dfrac{AB}{2}(h_1+h_2)=\dfrac{AB\cdot AD}{2}\\ Analog, \; S_{MAD}+S_{MBC}=\dfrac{AB\cdot AD}{2}\; , de\; unde\; rezulta\; concluzia[/tex]