1. **State the problem:** We are given the coordinates of the vertices of a quadrilateral representing a town's park: $(-9,0)$, $(-8,4)$, $(0,2)$, and $(-1,-2)$. We need to find the area of this quadrilateral. 2. **Formula used:** To find the area of a polygon given its vertices, we use the Shoelace formula: $$\text{Area} = \frac{1}{2} \left| \sum_{i=1}^{n} (x_i y_{i+1} - y_i x_{i+1}) \right|$$ where $(x_{n+1}, y_{n+1}) = (x_1, y_1)$ to close the polygon. 3. **List vertices in order:** Let's list the vertices in the order given: $$(-9,0), (-8,4), (0,2), (-1,-2)$$ 4. **Apply the Shoelace formula:** Calculate the sum of $x_i y_{i+1}$: $$(-9) \times 4 + (-8) \times 2 + 0 \times (-2) + (-1) \times 0 = -36 -16 + 0 + 0 = -52$$ Calculate the sum of $y_i x_{i+1}$: $$0 \times (-8) + 4 \times 0 + 2 \times (-1) + (-2) \times (-9) = 0 + 0 - 2 + 18 = 16$$ 5. **Calculate the area:** $$\text{Area} = \frac{1}{2} |(-52) - 16| = \frac{1}{2} |-68| = \frac{68}{2} = 34$$ 6. **Interpretation:** The area of the town's park is 34 square units.