[tex]\it \mathcal{A}=\sqrt{p(p-a)(p-b)(p-c)}\\ \\ p=\dfrac{9+13+10}{2}=16\\ \\ p-a=16-10=6\\ \\ p-b=16-3=3\\ \\ p-c=16-9=7\\ \\ \mathcal{A}=\sqrt{16\cdot6\cdot3\cdot7}=\sqrt{16\cdot9\cdot2\cdot4}=4\cdot3\sqrt{14}=12\sqrt{14}\ cm^2[/tex]
Fie AD - înălțimea dusă din A.
[tex]\it \mathcal{A}=\dfrac{BC\cdot AD}{2} \Rightarrow 12\sqrt{14}=\dfrac{10\cdot AD}{2}|_{\cdot2} \Rightarrow 24\sqrt{14}=10\cdot AD|_{:10} \Rightarrow \\ \\ \\ \Rightarrow AD=2,4\sqrt{14}\ cm[/tex]
