1. **Stating the problem:** We have a polygon with points C, S, D, R, and A connected by segments with given lengths: CA = 36 m, SR = 13 m, DR = 48 m, and SD = 7 m. We need to find the perimeter $P$, area $A$, and length $ST$. 2. **Understanding the shape and given data:** - CA is horizontal and 36 m long. - SR is horizontal and 13 m long. - DR is horizontal and 48 m long. - SD is 7 m long. - The polygon is formed by points C, S, D, R, and A. 3. **Finding the perimeter $P$:** The perimeter is the sum of all side lengths. We know CA = 36 m, SR = 13 m, DR = 48 m, SD = 7 m. We need to find lengths CS and AR to complete the perimeter. 4. **Finding length $CS$:** Since CA is 36 m and SR is 13 m, and the polygon is connected, we can infer that CS = CA - SR = $36 - 13 = 23$ m. 5. **Finding length $AR$:** Similarly, DR is 48 m and SD is 7 m, so AR = DR - SD = $48 - 7 = 41$ m. 6. **Calculating perimeter $P$:** $$P = CA + AS + SD + DR + RC$$ But we need to clarify the order of points. Assuming the polygon is C-S-D-R-A-C, the sides are: - CS = 23 m - SD = 7 m - DR = 48 m - RA = 41 m - AC = 36 m So, $$P = 23 + 7 + 48 + 41 + 36 = 155$$ m 7. **Finding area $A$:** We can divide the polygon into simpler shapes (triangles or rectangles) or use coordinate geometry. Assuming the polygon is irregular, we can use the shoelace formula if coordinates are known, but since only lengths are given, we need more info or assumptions. 8. **Finding length $ST$:** The problem asks for $ST$ but no length or position for $T$ is given, so we cannot determine $ST$ without additional information. **Final answers:** - Perimeter $P = 155$ m - Area $A$ cannot be determined with given data - Length $ST$ cannot be determined with given data