1. **State the problem:** We have a polygon with an area of 129 cm² and some given side lengths, including an unknown length $x$. We need to find $x$. 2. **Analyze the shape:** The polygon can be divided into two rectangles stacked vertically. - The left vertical side is 9 cm. - The right vertical side is 6 cm. - The top middle horizontal segment is 12 cm. - The bottom right horizontal segment is $x$ cm. 3. **Divide the shape:** - The top rectangle has height $9 - 6 = 3$ cm (difference between left and right vertical sides). - The bottom rectangle has height 6 cm. 4. **Calculate areas of rectangles:** - Top rectangle area = height \times width = $3 \times 12 = 36$ cm². - Bottom rectangle area = height \times width = $6 \times x = 6x$ cm². 5. **Write the total area equation:** $$36 + 6x = 129$$ 6. **Solve for $x$:** $$6x = 129 - 36$$ $$6x = 93$$ $$\cancel{6}x = \cancel{6} \times 15.5$$ $$x = 15.5$$ 7. **Answer:** The value of $x$ is $15.5$ cm.