Question

2. Diagonala cubului ABCDA'B'C'D' este √2, aflați aria şi diagonala unei fete.​

Answer 1

$d = l \sqrt{3} < = > \sqrt{2} = l \sqrt{3} < = > l = \frac{ \sqrt{3} }{ \sqrt{2} } = \frac{ \sqrt{6} }{2} \\ ab' = l \sqrt{2} = \sqrt{2} \times \frac{ \sqrt{6} }{2} = \sqrt{2} \times \frac{ \sqrt{2} \times \sqrt{3} }{2} = \frac{2 \sqrt{3} }{2} = \sqrt{3} \\ aria \: abb'a' = {l}^{2} = ( { \frac{ \sqrt{6} }{2}) }^{2} = \frac{6}{4} = \frac{3}{2} {cm}^{2}$