1. **State the problem:** We need to find the perimeter of a figure composed of a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Identify given dimensions:** The rectangle has length $9$ units and width $4$ units. Each semicircle has a diameter equal to the width of the rectangle, which is $4$ units. 3. **Recall formulas:** - Perimeter of rectangle without semicircles: $2(\text{length} + \text{width})$ - Circumference of a full circle: $C = \pi d$ - Circumference of a semicircle: $\frac{1}{2} \pi d$ 4. **Calculate the perimeter:** - The figure's perimeter includes the two lengths of the rectangle (each $9$ units) plus the circumference of the two semicircles combined (which make a full circle). 5. **Calculate the total semicircle perimeter:** $$\text{Perimeter of two semicircles} = \pi \times 4 = 4\pi$$ 6. **Calculate the total perimeter:** $$P = 2 \times 9 + 4\pi = 18 + 4\pi$$ 7. **Approximate the value:** $$P \approx 18 + 4 \times 3.1416 = 18 + 12.5664 = 30.5664$$ 8. **Round to the nearest tenth:** $$P \approx 30.6$$ **Final answer:** The perimeter of the figure is approximately $30.6$ units.