Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Problem Solving - Page 208: 41

The area of the triangular region is $12m^2$.

$A(0,0)$ $B(5, 2)$ $C(3, 6)$ $A_{ABC}=\pm\frac{1}{2}\begin{vmatrix} 0 &0 & 1\\ 5 &2 & 1 \\ 3 & 6 & 1 \end{vmatrix}$ $=\pm\frac{1}{2}[0(2-36)-0(5-3)+1(30-6)]$ $=\pm\frac{1}{2}(24)$ $=\pm12$ Hence $A_{ABC}=12$. The area of the triangular region is $12m^2$.