Question

Sa se calculeze aria triunghiului ABC, A(3,1), B(9,5),C(5,-3).

Answer 1

[tex]A= \frac{1}{2} *modul(\triangle)= \frac{1}{2} *modul(-32)=16,\ unde \\ \triangle= \left[\begin{array}{ccc}3&1&1\\9&5&1\\5&-3&1\end{array}\right] =-32[/tex]

Answer 2

[tex]A= \frac{1}{2}*|delta| [/tex]

delta=[tex] \left[\begin{array}{ccc}1&1&1\\3&9&5\\1&5&-3\end{array}\right] = -27+5+15-(9+25-9)=-27+5+15-9-25+9=-32[/tex]

$A= \frac{1}{2}*|-32|= \frac{1}{2}*32 = \frac{32}{2}= 16$