[tex]Folosim \: formula \: lui \: Heron [/tex]
[tex]a = 6 \: cm[/tex]
[tex]b = 5 \: cm[/tex]
[tex]c = \sqrt{13} \: cm[/tex]
[tex]A = \sqrt{p(p - a)(p - b)(p - c)} [/tex]
[tex]p = \frac{a + b + c}{2} = \frac{6 + 5 + \sqrt{13} }{2} = \frac{11 + \sqrt{13} }{2} [/tex]
[tex]A = \sqrt{ \frac{11 + \sqrt{13} }{2} ( \frac{11 + \sqrt{13} }{2} - 6)( \frac{11 + \sqrt{13} }{2} - 5)( \frac{11 + \sqrt{13} }{2} - \sqrt{13} )} [/tex]
[tex]A = \sqrt{ \frac{11 + \sqrt{13} }{2} \times \frac{11 + \sqrt{13} - 12}{2} \times \frac{11 + \sqrt{13} - 10 }{2} \times \frac{11 + \sqrt{13} - 2 \sqrt{13} }{2} } [/tex]
[tex]A = \sqrt{ \frac{11 + \sqrt{13} }{2} \times \frac{ \sqrt{13} - 1}{2} \times \frac{ \sqrt{13} + 1}{2} \times \frac{11 - \sqrt{13} }{2} } [/tex]
[tex]A = \sqrt{ \frac{(11 + \sqrt{13})(11 - \sqrt{13} )( \sqrt{13} - 1)( \sqrt{13} + 1)}{2} } [/tex]
[tex]A = \sqrt{ \frac{(121 - 13)(13 - 1)}{2} } [/tex]
[tex]A = \sqrt{ \frac{108 \times 12}{2} } [/tex]
[tex]A = \sqrt{108 \times 6} [/tex]
[tex]A = \sqrt{648} [/tex]
[tex]A = 18 \sqrt{2} \: {cm}^{2} [/tex]
