1. **State the problem:** We have two similar pentagons ABCDE and RSTUV. We know some side lengths of ABCDE and one side length of RSTUV (TU = 33 cm). We need to find the length of side RV in pentagon RSTUV. 2. **Recall the property of similar polygons:** Corresponding sides of similar polygons are proportional. This means the ratio of any side in ABCDE to its corresponding side in RSTUV is the same. 3. **Identify corresponding sides:** Given the order of vertices, side DE in ABCDE corresponds to side TU in RSTUV, and side EA corresponds to side RV. 4. **Write the proportion using known sides:** $$\frac{DE}{TU} = \frac{EA}{RV}$$ Given: $DE = 13.2$ cm, $TU = 33$ cm, $EA = 2.2$ cm, and $RV$ is unknown. 5. **Set up the equation:** $$\frac{13.2}{33} = \frac{2.2}{RV}$$ 6. **Cross multiply to solve for $RV$:** $$13.2 \times RV = 33 \times 2.2$$ 7. **Calculate the right side:** $$33 \times 2.2 = 72.6$$ 8. **Solve for $RV$:** $$RV = \frac{72.6}{13.2}$$ 9. **Simplify the fraction:** $$RV = \frac{\cancel{72.6}}{\cancel{13.2}} = 5.5$$ 10. **Final answer:** $$RV = 5.5 \text{ cm}$$ This means the length of side RV is 5.5 cm.