[tex]\displaystyle 7a) \\
\text{Se da: } \\
AB=5~cm \\
BC = 6 cm \\
\ \textless \ B = 30^o \\
\text{Se cere: } \\
A_{\Delta ABC} =? \\ \\
\text{Rezolvare: } \\ \\
A_{\Delta ABC} = \frac{AB\times AC\times \sin B}{2}=\frac{5\times 6\times \frac{1}{2} }{2}= \frac{30}{4}= \boxed{7,5~cm^2} [/tex]
[tex]\displaystyle 7b) \\
\text{Se da: } \\
AB=AC=BC=12~dm \\
\text{Se cere: } \\
A_{\Delta ABC} =? \\ \\
\text{Rezolvare: } \\ \\
A_{\Delta ABC} = \frac{AB^2\times \sqrt{3} }{2}= \frac{12^2\times \sqrt{3} }{2}= \frac{144 \sqrt{3} }{2}= \boxed{72\sqrt{3} ~dm^2} [/tex]
[tex]\displaystyle 7c) \\
\text{Se da: } \\
AB=4 \sqrt{6} ~m \\
AC=BC \\
\ \textless \ C = 90^o \\
\text{Se cere: } \\ A_{\Delta ABC} =? \\ \\
\text{Rezolvare: } \\ \\
A_{\Delta ABC} = \frac{AB^2}{4}=\frac{(4 \sqrt{6} )^2}{4}= \frac{96}{4}= \boxed{24~m^2}[/tex]
[tex]\displaystyle 7d) \\ \text{Se da: } \\
AB=6~cm \\
AC = 9m \\
BC = 11 m \\
\text{Se cere: } \\
A_{\Delta ABC} =? \\ \\
\text{Rezolvare: } \\ \\
P = AB+AC+BC=6+9+11 = 26~m\\ \\
p = \frac{P}{2} = \frac{26}{2} = 13\\ \\
A_{\Delta ABC} = \sqrt{p(p-AB)(p-AC)(p-BC)} = \\
=\sqrt{13(13-6)(13-9)(13-11)}= \\
=\sqrt{13 \times 7 \times 4 \times 2}= \\
2\sqrt{13 \times 7 \times 2}=2\sqrt{13 \times 7 \times 2}=2\sqrt{13 \times 14} = \boxed{2\sqrt{182}~m^2} [/tex]
