1. **State the problem:** Find the area of the polygon formed by the points $(-5,-4)$, $(2,-2)$, and $(1,3)$. Since there are three points, the polygon is a triangle. 2. **Formula used:** The area of a polygon given coordinates $(x_1,y_1), (x_2,y_2), \ldots, (x_n,y_n)$ can be found using the shoelace formula: $$\text{Area} = \frac{1}{2} \left| \sum_{i=1}^{n-1} (x_i y_{i+1} - y_i x_{i+1}) + (x_n y_1 - y_n x_1) \right|$$ 3. **Apply the formula:** For points $A(-5,-4)$, $B(2,-2)$, and $C(1,3)$: $$\begin{aligned} \text{Area} &= \frac{1}{2} |(-5)(-2) + 2 \cdot 3 + 1 \cdot (-4) - (-4) \cdot 2 - (-2) \cdot 1 - 3 \cdot (-5)| \\ &= \frac{1}{2} |10 + 6 - 4 + 8 + 2 + 15| \\ &= \frac{1}{2} |37| = 18.5 \end{aligned}$$ 4. **Explanation:** We multiply coordinates diagonally, sum them, subtract the reverse diagonal products, take the absolute value, and divide by 2 to get the polygon's area. **Final answer:** The area of the triangle is $18.5$ square units.