1. **State the problem:** We have two similar rectangles. The smaller rectangle has dimensions $4 \text{ cm}$ by $7 \text{ cm}$. The larger rectangle has one side $4.8 \text{ cm}$ and the other side unknown. We need to find the area of the larger rectangle. 2. **Understand similarity:** For similar rectangles, the ratio of corresponding sides is the same. 3. **Set up the ratio:** The side corresponding to $4 \text{ cm}$ is $4.8 \text{ cm}$, so the scale factor is: $$\text{scale} = \frac{4.8}{4} = 1.2$$ 4. **Find the unknown side:** The side corresponding to $7 \text{ cm}$ will be: $$7 \times 1.2 = 8.4 \text{ cm}$$ 5. **Calculate the area of the larger rectangle:** $$\text{Area} = 4.8 \times 8.4 = 40.32 \text{ cm}^2$$ 6. **Final answer:** The area of the larger rectangle is $40.32 \text{ cm}^2$.