1. **State the problem:** We are given a rectangular prism-like solid with a volume of 72.66 cubic inches and one dimension (height) of 2 inches. We need to find the area of the base (the polygonal end). 2. **Formula used:** The volume $V$ of a prism is given by the formula: $$V = B \times h$$ where $B$ is the area of the base and $h$ is the height. 3. **Given values:** $$V = 72.66 \text{ in}^3, \quad h = 2 \text{ in}$$ 4. **Find the base area $B$:** Rearranging the formula to solve for $B$: $$B = \frac{V}{h}$$ 5. **Substitute the known values:** $$B = \frac{72.66}{2}$$ 6. **Simplify the fraction:** $$B = \frac{\cancel{72.66}}{\cancel{2}} = 36.33$$ 7. **Final answer:** The area of the base is $$\boxed{36.33 \text{ in}^2}$$