1. **State the problem:** We have two similar rectangles, A and B. Rectangle A has an area of 39 and width 13. Rectangle B has width 4.55, and we need to find its area. 2. **Recall properties of similar rectangles:** For similar rectangles, the ratio of their corresponding sides is the same, and the ratio of their areas is the square of the ratio of their corresponding sides. 3. **Set up the ratio of widths:** $$ \text{Ratio of widths} = \frac{4.55}{13} $$ 4. **Calculate the ratio of areas:** $$ \text{Ratio of areas} = \left(\frac{4.55}{13}\right)^2 $$ 5. **Find the area of rectangle B:** $$ \text{Area}_B = \text{Area}_A \times \left(\frac{4.55}{13}\right)^2 = 39 \times \left(\frac{4.55}{13}\right)^2 $$ 6. **Simplify the fraction:** $$ \frac{4.55}{13} = \frac{\cancel{4.55}}{\cancel{13}} \approx 0.35 $$ 7. **Calculate the area:** $$ \text{Area}_B = 39 \times (0.35)^2 = 39 \times 0.1225 = 4.7775 $$ 8. **Final answer:** The area of rectangle B is approximately **4.78**.