Question

Calcule a área do triângulo que cujos vértices são os pontos A (6,10),B (-3,4) e C (6,-8).

Answer 1

A area é dada por:

$Area=\frac{1}{2}.\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right|\\\\\\Area=\frac{1}{2}.\left|\begin{array}{ccc}6&10&1\\-3&4&1\\6&-8&1\end{array}\right|\\\\\\Area=\frac{1}{2}\left[(\;\;6.4.1 + (-3).(-8).1+6.10.1\;\;)-(\;\;1.4.6+1.(-8).6+1.10.(-3)\;\;)\right]\\\\Area=\frac{1}{2}\left[(\;\;24 + 24+60\;\;)-(\;\;24-48-30\;\;)\right]\\\\Area=\frac{1}{2}\left[(\;\;108\;\;)-(\;\;-54\;\;)\right]\\\\Area=\frac{1}{2}\left[108+54\right]$

$Area=\frac{1}{2}\left[108+54\right]\\\\Area=\frac{1}{2}162\\\\Area=81$