1) Orice fata a unui tetraedru regulat este un triunghi echilateral.
Inaltimea h a unui triunghi echilateral este egala cu:
[tex]\displaystyle \\
h = l \times \frac{ \sqrt{3} }{2} =\frac{l \sqrt{3} }{2} [/tex]
Aria triunghiului echilateral este:
[tex]\displaystyle \\
A = \frac{B \times h}{2} = \frac{l \times h}{2} = \frac{l \times \frac{l \sqrt{3} }{2}}{2} = \frac{l^2 \sqrt{3} }{4}=\frac{6^2 \sqrt{3} }{4}=\frac{36 \sqrt{3} }{4}= \boxed{9 \sqrt{3}~cm^2 }[/tex]
2) [tex] \sqrt{2} \times \sqrt{5} = \sqrt{2\times 5} = \boxed{\sqrt{10}} [/tex]
