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Área de um triângulo no plano cartesiano
[tex]\Large\boxed{\begin{array}{c}\sf Sejam~A(x_A,y_A),B(x_B,y_B)~C(x_C,y_C)\\\sf os~3~v\acute ertices~de~um~tri\hat angulo~no~plano~cartesiano.\\\sf a~\acute area~deste~tri\hat angulo~\acute e~dada~por: A=\dfrac{|det~M|}{2}\\\sf sendo~M=\begin{bmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{bmatrix}\end{array}}[/tex]
[tex]\sf M=\begin{bmatrix}\sf1&\sf3&\sf1\\\sf7&\sf1&\sf1\\\sf3&\sf5&\sf1\end{bmatrix}\\\sf det~M=1\cdot(1-5)-3\cdot(7-3)+1\cdot(35-3)\\\sf det~M=-4-12+32\\\sf det~M=16\\\sf A=\dfrac{|det~M|}{2}\\\sf A=\dfrac{16}{2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf A=8~u\cdot a}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~ d}}}}[/tex]
