1. **Problem Statement:** Find the area of a figure composed of a rectangle and one semicircle added on the right side, with another semicircle removed on the left side. The rectangle has length 8 and height 4. Both semicircles have radius 4. 2. **Formulae and Important Rules:** - Area of rectangle: $A_{rect} = \text{length} \times \text{height}$ - Area of a full circle: $A_{circle} = \pi r^2$ - Area of a semicircle: $A_{semi} = \frac{1}{2} \pi r^2$ 3. **Calculate the area of the rectangle:** $$A_{rect} = 8 \times 4 = 32$$ 4. **Calculate the area of one semicircle (radius 4):** $$A_{semi} = \frac{1}{2} \pi (4)^2 = \frac{1}{2} \pi \times 16 = 8\pi$$ 5. **Calculate the total area of the figure:** The figure adds one semicircle on the right and removes one semicircle on the left, so the net semicircle area is: $$8\pi - 8\pi = 0$$ 6. **Final area:** Since the semicircle added and removed have the same area, they cancel out, so the total area is just the rectangle's area: $$\boxed{32}$$ 7. **Rounding:** The area is exactly 32, so rounded to the nearest tenth is 32.0.