1. **State the problem:** We need to find the area of a compound polygon composed of rectangles and a triangle with given side lengths. 2. **Identify the shapes and dimensions:** The figure consists of: - A left rectangle with dimensions 5 cm by 8 cm. - A top-right rectangle with dimensions 7 cm by 3 cm. - A right downward extension rectangle with dimensions 2 cm by 9 cm. - A lower right triangle with base 8 cm and height 5 cm. 3. **Formula for area:** - Rectangle area = length \times width - Triangle area = \frac{1}{2} \times base \times height 4. **Calculate each area:** - Left rectangle area = $5 \times 8 = 40$ cm$^2$ - Top-right rectangle area = $7 \times 3 = 21$ cm$^2$ - Right downward extension area = $2 \times 9 = 18$ cm$^2$ - Lower right triangle area = $\frac{1}{2} \times 8 \times 5 = 20$ cm$^2$ 5. **Sum all areas:** $$ \text{Total area} = 40 + 21 + 18 + 20 = 99 \text{ cm}^2 $$ 6. **Final answer:** The area of the figure is **99 square centimeters**.