Question

Calculați aria triunghiului abc
in cazurile
1a=5
b=7
c=11

Answer 1

Folosim formula lui Heron :

$a = 5$

$b = 7$

$c = 11$

$p = \frac{a + b + c}{2} = \frac{5 + 7 + 11}{2} = \frac{23}{2}$

$A = \sqrt{p(p - a)(p - b)(p - c)}$

$A = \sqrt{ \frac{23}{2} ( \frac{23}{2} - 5)( \frac{23}{2} - 7)( \frac{23}{2} - 11)}$

$A = \sqrt{ \frac{23}{2} ( \frac{23}{2} - \frac{10}{2} )( \frac{23}{2} - \frac{14}{2} )( \frac{23}{2} - \frac{22}{2}) }$

$A = \sqrt{ \frac{23}{2} \times \frac{13}{2} \times \frac{9}{2} \times \frac{1}{2} }$

$A = \sqrt{ \frac{2691}{16} }$

$A = \frac{ \sqrt{2691} }{ \sqrt{16} }$

$A = \frac{ \sqrt{2691} }{4}$