1. The problem shows a rectangle with sides labeled 8 and 4 on the top, and 4 and 2 on the bottom, and a circle inside it. We need to understand the relationship between these numbers and the rectangle. 2. First, let's clarify the rectangle's dimensions. The top side is divided into segments 8 and 4, so the total length of the top side is $8 + 4 = 12$. 3. The bottom side is divided into segments 4 and 2, so the total length of the bottom side is $4 + 2 = 6$. 4. Since opposite sides of a rectangle are equal, the rectangle's length is 12 and its width is 6. 5. The circle inside the rectangle could be inscribed or just placed inside. If the circle is inscribed, its diameter equals the smaller side of the rectangle, which is 6. 6. Therefore, the radius of the inscribed circle is $\frac{6}{2} = 3$. 7. The area of the rectangle is $12 \times 6 = 72$. 8. The area of the circle is $\pi r^2 = \pi \times 3^2 = 9\pi$. 9. This problem helps understand how to find dimensions from segment sums and relate inscribed shapes. Final answers: - Rectangle dimensions: length = 12, width = 6 - Radius of inscribed circle: 3 - Area of rectangle: 72 - Area of circle: $9\pi$