1. **State the problem:** We need to find the area of a figure composed of a rectangle and two semicircles attached on the shorter sides. 2. **Identify given dimensions:** The rectangle has length $12$ and width $4$. Each semicircle has a diameter equal to the width of the rectangle, which is $4$. 3. **Formula for area of rectangle:** $$\text{Area}_{rectangle} = \text{length} \times \text{width}$$ 4. **Formula for area of a circle:** $$\text{Area}_{circle} = \pi r^2$$ 5. **Calculate radius of semicircles:** $$r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2$$ 6. **Calculate area of rectangle:** $$\text{Area}_{rectangle} = 12 \times 4 = 48$$ 7. **Calculate area of one semicircle:** $$\text{Area}_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi \times 4 = 2\pi$$ 8. **Calculate area of two semicircles (which form a full circle):** $$2 \times 2\pi = 4\pi$$ 9. **Calculate total area:** $$\text{Area}_{total} = \text{Area}_{rectangle} + \text{Area}_{two\ semicircles} = 48 + 4\pi$$ 10. **Approximate numerical value:** $$4\pi \approx 4 \times 3.1416 = 12.5664$$ $$\text{Area}_{total} \approx 48 + 12.5664 = 60.5664$$ Rounded to the nearest tenth: $$60.6$$ **Final answer:** The area of the figure is approximately $60.6$ square units.