Question

Um terreno plano tem as coordenadas de seus vértices dadas na figura.

Answer 1

 Traçando uma das diagonais do quadrilátero, obtemos 2 triângulos

Sendo os pontos  do primeiro

A(8,8)
B(2,4)
C(9,2)

$\left[\begin{array}{ccc}x_A&y_A&1\\x_B& y_B&1\\x_C&y_C&1\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccc}8&8&1\\2&4&1\\9&2&1\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccccc}8&8&1&8&8\\2&4&1&2&4\\9&2&1&9&2\end{array}\right] =32+72+4-(36+16+16)=108-68=\fbox{ 40 }$ 

pontos do outro triângulo 

A(8,8)
C(9,2)
D(20,6)

$\left[\begin{array}{ccc}x_A&y_A&1\\x_C&y_C&1\\x_D&y_D&1\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccc}8&8&1\\9&2&1\\20&6&1\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccccc}8&8&1&8&8\\9&2&1&9&2\\20&6&1&20&6\end{array}\right] =$ 

$D=16+160+54-(40+48+72)=230-160=70$ 


$\'area= \frac{1}{2} (|D_1|+|D_2|) \\ \\ A= \frac{1}{2} (40+70) \\ \\ A= \frac{110}{2} \\ \\ \'area=55m^2~~~\mapsto letra~~C$