Question

determine a area do triangulo de vertices A(2,3), B(5,4) e C(6,-3)

Answer 1

Podemos calcular pela expressão:

$Area=\frac{1}{2}.\left|\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right| \right|\\\\\\Area=\frac{1}{2}.\left|\left|\begin{array}{ccc}2&3&1\\5&4&1\\6&-3&1\end{array}\right| \right|\\\\Area=\frac{1}{2}.|2.4.1+5.(-3).1+6.3.1-1.4.6-1.(-3).2-1.3.5|\\\\Area=\frac{1}{2}.|8+(-15)+18-24-(-6)-15|\\\\Area=\frac{1}{2}.|8-15+18-24+6-15|\\\\Area=\frac{1}{2}.|-22|\\\\Area=\frac{1}{2}.22\\\\Area = 11\;u.a.$