1. **State the problem:** Find the area of a composite shape consisting of a rectangle and a semicircle on top. 2. **Identify dimensions:** The rectangle is 3 units wide and 4 units tall. The semicircle has a diameter of 3 units, so its radius is $r = \frac{3}{2} = 1.5$ units. 3. **Formula for area of rectangle:** $$A_{rectangle} = \text{width} \times \text{height} = 3 \times 4 = 12$$ 4. **Formula for area of semicircle:** The area of a full circle is $\pi r^2$, so the area of a semicircle is half of that: $$A_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (1.5)^2 = \frac{1}{2} \pi \times 2.25 = 1.125\pi$$ 5. **Calculate total area:** $$A_{total} = A_{rectangle} + A_{semicircle} = 12 + 1.125\pi$$ 6. **Approximate numerical value:** Using $\pi \approx 3.1416$, $$A_{total} \approx 12 + 1.125 \times 3.1416 = 12 + 3.5346 = 15.5346$$ **Final answer:** The area of the composite shape is approximately $15.53$ square units.