1. **Stating the problem:** We are asked to find the lengths of segments RS and EC (part c), and then find the lengths of PQ, AF, and MT (part d) based on the given measurements. 2. **Understanding the problem:** The problem involves finding unknown segment lengths in a geometric figure with given side lengths. We will use properties of triangles, segments, and possibly the Pythagorean theorem or segment addition. 3. **Finding RS and EC:** - Given RS = 4 cm (from the problem statement). - EC is given as 6 cm. So, RS = 4 cm and EC = 6 cm directly from the data. 4. **Finding PQ, AF, and MT:** - PQ is given as 3.2 cm or 8 cm in different parts; assuming PQ = 8 cm as per the last data. - AF is not directly given; if AF is part of a segment with total length and other parts known, use subtraction. - MT is given as 4 cm. Since the problem data is fragmented, we assume: - PQ = 8 cm - MT = 4 cm - AF = 5 cm (from the data near E and B) 5. **Summary of lengths:** - RS = 4 cm - EC = 6 cm - PQ = 8 cm - AF = 5 cm - MT = 4 cm **Final answers:** $$RS = 4\ \text{cm},\quad EC = 6\ \text{cm},\quad PQ = 8\ \text{cm},\quad AF = 5\ \text{cm},\quad MT = 4\ \text{cm}$$