1. **State the problem:** We have two concentric circles. The inner circle has radius $19$ yd, and the ring-shaped path around it has a width of $5$ yd. We want to find the area of the ring-shaped path. 2. **Formula used:** The area of a ring (annulus) is the difference between the areas of the outer and inner circles. $$\text{Area} = \pi R^2 - \pi r^2 = \pi (R^2 - r^2)$$ where $R$ is the outer radius and $r$ is the inner radius. 3. **Find the outer radius:** $$R = r + \text{width} = 19 + 5 = 24 \text{ yd}$$ 4. **Calculate the area of the ring:** $$\text{Area} = \pi (24^2 - 19^2) = \pi (576 - 361) = \pi \times 215$$ 5. **Final answer:** $$\text{Area} = 215\pi \text{ yd}^2$$ This is the exact area of the ring-shaped path between the two circles.