1. The problem gives two teardrop-shaped closed curves with areas and perimeters: - Bottom shape: area $A_1 = 7$ cm$^2$, perimeter $P_1 = 9$ cm - Top shape: area $A_2 = 14$ cm$^2$, perimeter $P_2 = 12$ cm 2. We want to analyze or compare these shapes based on the given data. 3. One useful measure is the isoperimetric ratio, which compares area and perimeter to assess shape efficiency: $$\text{Isoperimetric ratio} = \frac{4\pi \times \text{Area}}{(\text{Perimeter})^2}$$ 4. Calculate for bottom shape: $$\frac{4\pi \times 7}{9^2} = \frac{28\pi}{81} \approx 1.086\n$$ 5. Calculate for top shape: $$\frac{4\pi \times 14}{12^2} = \frac{56\pi}{144} = \frac{14\pi}{36} \approx 1.221$$ 6. Since the isoperimetric ratio is closer to 1 for the top shape, it is more efficient in enclosing area relative to its perimeter. 7. This suggests the top shape is closer to a circle in shape than the bottom one. Final answer: The top shape with area 14 cm$^2$ and perimeter 12 cm has a higher isoperimetric ratio ($\approx 1.221$) than the bottom shape ($\approx 1.086$), indicating it is more area-efficient relative to its perimeter.