1. **Problem Statement:** Given two congruent polygons ABCD and AFED, with C as the midpoint of segment MD, and MC = 3 cm, find the length of AE. 2. **Understanding the problem:** Since polygons ABCD and AFED are congruent, corresponding sides and angles are equal. 3. **Key information:** - C is midpoint of MD, so MC = CD = 3 cm. - MC = 3 cm given. - Polygons ABCD and AFED are congruent, so side AE corresponds to side BC or CD. 4. **Using congruence:** Since ABCD ≅ AFED, side AE corresponds to side BC or CD. Given C is midpoint of MD, and MC = 3 cm, then CD = 3 cm. 5. **Finding AE:** Since AE corresponds to BC or CD, and CD = 3 cm, AE = 3 cm. **Final answer:** AE = 3 cm. Therefore, the correct choice is (a) 3 cm.