1. **State the problem:** Calculate the perimeter and area of an irregular L-shaped polygon with given side lengths: vertical left edge = 10.7 yd, top horizontal segment = 1.9 yd, vertical right edge = 6.9 yd, and bottom horizontal edge = 9.1 yd. 2. **Calculate the perimeter:** The perimeter is the total length around the polygon. We add all the outer edges. Given edges: 10.7 yd (left vertical), 1.9 yd (top horizontal), 6.9 yd (right vertical), 9.1 yd (bottom horizontal), and the missing horizontal segment between the vertical edges. 3. **Find the missing horizontal segment:** The total vertical height is 10.7 yd on the left and 6.9 yd on the right. The difference is $$10.7 - 6.9 = 3.8$$ yd, which corresponds to the vertical segment connecting the two horizontal segments. 4. **Calculate the missing horizontal segment:** The bottom horizontal edge is 9.1 yd, and the top horizontal segment is 1.9 yd. The missing horizontal segment is $$9.1 - 1.9 = 7.2$$ yd. 5. **Sum all edges for perimeter:** $$P = 10.7 + 1.9 + 6.9 + 7.2 + 9.1 = 35.8$$ yd 6. **Calculate the area:** Break the L-shape into two rectangles. - Rectangle 1 (top): width = 1.9 yd, height = 6.9 yd - Rectangle 2 (bottom): width = 7.2 yd, height = 3.8 yd 7. **Calculate areas of rectangles:** $$A_1 = 1.9 \times 6.9 = 13.11$$ yd² $$A_2 = 7.2 \times 3.8 = 27.36$$ yd² 8. **Total area:** $$A = A_1 + A_2 = 13.11 + 27.36 = 40.47$$ yd² **Final answers:** - Perimeter = 35.8 yd - Area = 40.47 yd²