ANSWER
The area of triangle DEF is [tex]12[/tex] square units.
EXPLANATION
The area of triangle DEF can be found using the formula,
[tex]Area=\frac{1}{2}\times base \times height[/tex].
From the diagram, we can see that the height of the triangle is bounded between [tex]x=-7[/tex] and [tex]x=-11[/tex].
We use the absolute value method to find the height to be,
[tex]Height=|-7--11|=|-7+11|=|4|=4[/tex].
The base of the triangle is |DE|.
We can again use the absolute value method to to determine the length of the base to be,
[tex]Length=|9-3|=|6|=6[/tex]
We now calculate the area to obtain,
[tex]Area=\frac{1}{2}\times 6\times 4 =3\times 12=12[/tex]
Therefore the area of the triangle 12 square units
