1. **State the problem:** We need to find the area of a four-lobed shape formed by four semicircles each with radius $0.5$ cm arranged around a central square, with the total height of the shape being $1$ cm. 2. **Understand the shape:** The shape consists of a central square and four semicircles attached to each side of the square. Each semicircle has radius $r=0.5$ cm. 3. **Calculate the area of the central square:** Since the height of the entire shape is $1$ cm and the semicircles extend $0.5$ cm above and below the square, the side length of the square is $1 - 2 \times 0.5 = 0$ cm. But the problem states the shape occupies the middle 4 squares in a plus-sign arrangement, so the central square side length is $1$ cm. 4. **Calculate the area of the square:** $$\text{Area}_{square} = 1 \times 1 = 1 \text{ cm}^2$$ 5. **Calculate the area of one semicircle:** $$\text{Area}_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (0.5)^2 = \frac{1}{2} \pi \times 0.25 = 0.125\pi \text{ cm}^2$$ 6. **Calculate the total area of four semicircles:** $$4 \times 0.125\pi = 0.5\pi \text{ cm}^2$$ 7. **Calculate the total area of the shape:** $$\text{Area}_{total} = \text{Area}_{square} + \text{Area}_{semicircles} = 1 + 0.5\pi$$ 8. **Evaluate the numerical value:** $$1 + 0.5 \times 3.1416 = 1 + 1.5708 = 2.5708 \text{ cm}^2$$ 9. **Round to the nearest 0.1 cm²:** $$2.6 \text{ cm}^2$$ **Final answer:** The area of the shape is approximately $2.6$ cm².