Question

Calcule a aerea do triangulo que passa pelos pontos A(0,0), B(4,0) e C(0,3)

Answer 1

Dados os tres vértices do triangulo, podemos calcular sua área pelo método do determinante, acompanhe:

$Area~=~\frac{1}{2}~.~\left|\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right| \right|\\\\\\\\Area~=~\frac{1}{2}~.~\left|\left|\begin{array}{ccc}0&0&1\\4&0&1\\0&3&1\end{array}\right| \right|\\\\\\Area~=~\frac{1}{2}~.~\left|~(~0.0.1+4.3.1+0.0.1~)~-~(~1.0.0+1.3.0+1.0.4~)~\right|\\\\\\Area~=~\frac{1}{2}~.~\left|~(~0+12+0~)~-~(~0+0+0~)~\right|\\\\\\Area~=~\frac{1}{2}~.~\left|~12~-~0~\right|\\\\\\Area~=~\frac{1}{2}~.~12\\\\\\\boxed{Area~=~6~unidades~de~area}$