The vertices are given as D(-8,4), E(-2,2), and F(-5,9).
Consider that area of the traingle is given by,
[tex]\text{Area}=\frac{1}{2}\lbrack x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\rbrack[/tex]Then the area of triangle DEF is given by,
[tex]\text{Area}=\frac{1}{2}\lbrack-8(2-9)-2(9-4)-5_{}(4-2)\rbrack=\frac{1}{2}\lbrack-8(-7)-2(5)-5(2)\rbrack[/tex]Simplify the terms further as,
[tex]\text{Area}=\frac{1}{2}\lbrack56-10-10\rbrack=\frac{1}{2}(36)=18[/tex]Thus, the area of the triangle is 18 square units.
