1. The problem involves finding the area and perimeter of an L-shaped polygon with given side lengths: 12 in (top), 19 in (right), 7 in (left), and 6 in (inner horizontal segment). 2. The perimeter is given as 50 in, and we need to confirm if the 6 in segment is on the right side. 3. In an L-shaped polygon, the inner horizontal segment (6 in) is typically on the right side, connecting the vertical sides. 4. To verify, sum the known sides: top (12) + right (19) + left (7) + inner horizontal (6) + bottom segment (unknown). 5. Since perimeter = sum of all outer sides, and given perimeter = 50, we find the missing bottom segment length: $$\text{Bottom segment} = 50 - (12 + 19 + 7 + 6) = 50 - 44 = 6$$ 6. This confirms the 6 in segment is indeed on the right side as the inner horizontal segment. 7. Therefore, the 6 in segment is correctly placed on the right side of the polygon. 8. To find the area, split the L-shape into two rectangles: - Rectangle 1: width 12 in, height 7 in - Rectangle 2: width 6 in, height (19 - 7) = 12 in 9. Calculate areas: $$\text{Area}_1 = 12 \times 7 = 84$$ $$\text{Area}_2 = 6 \times 12 = 72$$ 10. Total area: $$\text{Area} = 84 + 72 = 156$$ Final answers: - Area = 156 square inches - Perimeter = 50 inches