1. **Problem Statement:** Find the area of the large semicircle given smaller semicircle and quarter circle inside it, each labeled with radius 4. 2. **Understanding the problem:** The large semicircle contains a smaller semicircle and a quarter circle, both with radius 4. The large semicircle spans the entire width, so its diameter equals the sum of the diameters of the smaller semicircle and quarter circle. 3. **Formula for area of a semicircle:** $$\text{Area} = \frac{1}{2} \pi r^2$$ where $r$ is the radius. 4. **Determine the radius of the large semicircle:** - The smaller semicircle has radius 4, so diameter is $2 \times 4 = 8$. - The quarter circle also has radius 4, so its diameter is also 8. - The large semicircle's diameter is the sum of these diameters: $8 + 8 = 16$. - Therefore, the radius of the large semicircle is $\frac{16}{2} = 8$. 5. **Calculate the area of the large semicircle:** $$\text{Area} = \frac{1}{2} \pi (8)^2 = \frac{1}{2} \pi \times 64 = 32\pi$$ 6. **Final answer:** The area of the large semicircle is $32\pi$ square units.