Explicație pas cu pas:
1) ABC triunghi echilateral:
[tex]\ell = 4 \ \ cm \\ \implies P = 3 \cdot \ell = 3 \cdot 4 = \bf 12 \ \ cm[/tex]
2) OC bisectoare:
[tex]m(∢COB) = \frac{1}{2} \cdot m(∢AOB) = \frac{140}{2} \\ \implies \bf m(∢COB) = 70 \degree[/tex]
3) AB = 6 cm, m(∢B) = 30°, Aria = 18 cm²
[tex]Aria = \frac{AB \cdot BC \cdot sin \angle B}{2} \iff \\ 18 = \frac{6 \cdot BC \cdot \frac{1}{2} }{2} \implies BC = \bf 12 \: cm[/tex]
4) ABCDEF hexagon regulat, AB = 12 cm
AB ≡ OF => OF = 12 cm
FC = 2×OF = 2×12 = 24 => FC = 24 cm
5) ABCD dreptunghi, AC = 2BC
AC = 2×OC => OC ≡ BC ≡ OB
=> ΔBOC echilateral
=> m(∢BOC) = 60°
6) ABCD pătrat, aria = 72 cm²
[tex]aria = {\ell}^{2} \implies \ell = 6 \sqrt{2} \ \ cm[/tex]
[tex]d = \ell \sqrt{2} = 6 \sqrt{2} \cdot \sqrt{2} = \bf 12 \: cm[/tex]
