1. **State the problem:** We need to find the perimeter of a figure composed of a rectangle and two semicircles attached to the vertical ends of the rectangle. 2. **Identify given dimensions:** The rectangle has length $12$ units and height $4$ units. Each semicircle has a diameter equal to the height of the rectangle, which is $4$ units. 3. **Recall formulas:** - Perimeter of rectangle (without semicircles) is $2(\text{length} + \text{height})$. - Circumference of a full circle is $2\pi r$. - Perimeter contribution of two semicircles equals the circumference of one full circle with diameter $4$ units. 4. **Calculate radius of semicircles:** $$r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2$$ 5. **Calculate circumference of full circle formed by two semicircles:** $$2\pi r = 2\pi \times 2 = 4\pi$$ 6. **Calculate perimeter of rectangle excluding the vertical sides (since semicircles replace them):** The two vertical sides of length $4$ each are replaced by semicircles, so only the two horizontal sides contribute: $$2 \times 12 = 24$$ 7. **Calculate total perimeter:** $$\text{Perimeter} = \text{horizontal sides} + \text{semicircles circumference} = 24 + 4\pi$$ 8. **Approximate numerical value:** $$4\pi \approx 4 \times 3.1416 = 12.5664$$ $$\text{Perimeter} \approx 24 + 12.5664 = 36.5664$$ 9. **Round to nearest tenth:** $$36.6$$ **Final answer:** The perimeter of the figure is approximately $36.6$ units.