Question

10-Calcule a área do quadrilátero ABCD, sabendo-se que seus vértices são os pontos A( 2 , 0), B(3 , 1) , C( 1 , 4) e D( 0 , 2) .

Answer 1

$\large\boxed{\begin{array}{l}\sf M=\begin{vmatrix}\sf2&\sf0\\\sf3&\sf1\\\sf1&\sf4\\\sf0&\sf2\\\sf2&\sf0\end{vmatrix}\\\\\sf det M_{direita}=2+12+2+0=16\\\sf detM_{esquerda}=0+1+0+4=5\\\sf det~M=detM_{direita}-detM_{esquerda}=16-5=11\\\sf A=\dfrac{|det~M|}{2}\\\\\sf A=\dfrac{11}{2}\end{array}}$