1. **Stating the problem:** We have an L-shaped polygon with four sides: a left vertical side of 12 units, a bottom vertical side of 6 units, a right horizontal top side of 5 units, and a horizontal inner line of the lower part of 8 units. We want to find the area of this L-shaped polygon. 2. **Understanding the shape:** The L-shape can be divided into two rectangles. The first rectangle is the vertical part with height 12 units and width equal to the difference between the two horizontal segments (8 units + 5 units). The second rectangle is the horizontal part with height 6 units and width 8 units. 3. **Calculating the widths:** The total width of the top horizontal side is 5 units, and the inner horizontal line is 8 units. So the total width of the larger rectangle is $5 + 8 = 13$ units. 4. **Calculating the areas:** - Area of the larger rectangle (vertical part): height $12$ units, width $5$ units (since the right horizontal top side is 5 units). - Area of the smaller rectangle (horizontal part): height $6$ units, width $8$ units. 5. **Area of the L-shaped polygon:** $$\text{Area} = (12 \times 5) + (6 \times 8) = 60 + 48 = 108$$ 6. **Conclusion:** The area of the L-shaped polygon is $108$ square units.