find the area of the triangle in square units. round your answer to the hundredths place if necessary.

Explanation:

Step1: Identify vertex coordinates

From the graph: $A(-2, -3)$, $B(0, 9)$, $C(6, 8)$

Step2: Use shoelace formula

The shoelace formula for area of triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is: $$\text{Area} = \frac{1}{2}\left|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)\right|$$

Step3: Substitute values into formula

$$ \begin{align*} \text{Area} &= \frac{1}{2}\left|-2(9-8) + 0(8-(-3)) + 6(-3-9)\right|\ &= \frac{1}{2}\left|-2(1) + 0(11) + 6(-12)\right|\ &= \frac{1}{2}\left|-2 + 0 -72\right|\ &= \frac{1}{2}\left|-74\right| \end{align*} $$

Step4: Calculate final area

$$\text{Area} = \frac{1}{2} \times 74 = 37$$

Answer:

37 square units