1. **State the problem:** We need to find the area of an L-shaped polygon composed of three segments: a top horizontal segment of length 1, a right vertical segment of length $x$, and an inner vertical segment of length $x - 1$, with a bottom horizontal segment of length 2. 2. **Understand the shape:** The L-shape can be divided into two rectangles: - Rectangle A: width 1 (top horizontal segment) and height $x - 1$ (inner vertical segment). - Rectangle B: width 2 (bottom horizontal segment) and height 1 (difference between $x$ and $x - 1$). 3. **Calculate the area of Rectangle A:** $$\text{Area}_A = 1 \times (x - 1) = x - 1$$ 4. **Calculate the area of Rectangle B:** $$\text{Area}_B = 2 \times 1 = 2$$ 5. **Sum the areas to get total area:** $$\text{Area}_{total} = (x - 1) + 2 = x + 1$$ 6. **Final answer:** The area of the L-shaped polygon is $$\boxed{x + 1}$$.