Question

Calcule a área do triangulo a (0,0)b (0,4)c (3,2)

Answer 1

Podemos calcular a área do triangulo por:

$Area ~=~\frac{1}{2}~.~\left| \left| \begin{array}{ccc}a_x&a_y&1\\b_x&b_y&1\\c_x&c_y&1\end{array}\right| \right|\\\\\\Area ~=~\frac{1}{2}~.~\left|\left|\begin{array}{ccc}0&0&1\\0&4&1\\3&2&1\end{array}\right| \right|\\\\\\Area ~=~\frac{1}{2}~.~\left|~\left[(0.4.1~+~0.2.1~+~3.0.1)-(1.4.3~+~1.2.0~+~1.0.0)\right]~\right|\\\\\\Area ~=~\frac{1}{2}~.~\left|~\left[(0~+~0~+~0)-(12~+~0~+~0)\right]~\right|\\\\\\Area ~=~\frac{1}{2}~.~\left|~\left[(0-12)\right]~\right|$

$Area ~=~\frac{1}{2}~.~12\\\\\\\boxed{Area~=~6~unidades~de~area}$