1. **State the problem:** We need to find the perimeter of an irregular polygon shaped like a U with given side lengths: left vertical segment = 6 yd, right vertical segment inside the U = 5 yd, top right vertical segment = 3 yd, rightmost vertical segment = 8 yd, and bottom horizontal segment = 10 yd. The top left horizontal segment length is missing and must be found. 2. **Understand the perimeter:** The perimeter is the total distance around the polygon, which is the sum of all its side lengths. 3. **Identify missing side length:** The polygon has a top left horizontal segment missing. Since the bottom horizontal segment is 10 yd, and the top right horizontal segment is missing, we can find the missing top left horizontal segment by subtracting the top right horizontal segment from the bottom horizontal segment. 4. **Calculate the missing top left horizontal segment:** The top right horizontal segment is the difference between the bottom horizontal segment and the top left horizontal segment. But we only know the bottom horizontal segment (10 yd) and the vertical segments. To find the missing horizontal segment, note that the total vertical height on the right side is 3 yd + 8 yd = 11 yd, and the left vertical segment is 6 yd, so the difference in vertical height is 11 yd - 6 yd = 5 yd, which matches the right vertical segment inside the U. 5. **Sum all known sides:** The perimeter is the sum of all sides: left vertical (6 yd) + top left horizontal (unknown) + right vertical inside U (5 yd) + top right vertical (3 yd) + rightmost vertical (8 yd) + bottom horizontal (10 yd). 6. **Find the missing top left horizontal segment:** Since the polygon is closed, the top left horizontal segment plus the top right horizontal segment must equal the bottom horizontal segment (10 yd). The top right horizontal segment is missing, but the problem does not provide it. Assuming the top right horizontal segment is 0 (the polygon shape suggests the top right vertical segment is vertical, so the top right horizontal segment is 0), then the top left horizontal segment equals 10 yd. 7. **Calculate perimeter:** Add all sides: 6 + 10 + 5 + 3 + 8 + 10 = 42 yd. **Final answer:** The perimeter is 42 yards.