Question

Calcule a área da região do triângulo abaixo:​

Answer 1

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$\boxed{\begin{array}{l}\sf Seja~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf os~v\acute ertices~de~um~tri\hat angulo~no~plano~cartesiano.\\\sf A~\acute area~deste~tri\hat angulo~\acute e~dada~por\\\sf A=\dfrac{|det~M|}{2}\\\sf onde\\\sf M=\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}\end{array}}$

$\sf A(1.6)~~B(7,2)~C(-3,-2)\\\sf M=\begin{vmatrix}\sf1&\sf6&\sf1\\\sf7&\sf2&\sf1\\\sf-3&\sf-2&\sf1\end{vmatrix}\\\sf det~M=1\cdot(2+2)-6\cdot(7+3)+1\cdot(-14+6)\\\sf det~M=4-60-8\\\sf det~M=-64\\\sf A=\dfrac{|det~M}{2}\\\sf A=\dfrac{|-64|}{2}\\\sf A=\dfrac{64}{2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf A=32~u\cdot a}}}}$