1. **State the problem:** We need to find the area of an irregular polygon composed of rectangles and triangles with given side lengths in millimeters. 2. **Analyze the figure:** The polygon can be divided into simpler shapes whose areas we can calculate and then sum. 3. **Divide the figure:** - Left vertical section: a rectangle of width 2 mm and height 5 mm (top segment) plus a rectangle of width 2 mm and height 4 mm (middle segment). - Bottom left rectangle: width 3 mm and height 5 mm. - Right side: a rectangle of width 8 mm and height 9 mm minus a triangular section on top. - Top right triangle: base 8 mm and height 5 mm. 4. **Calculate areas:** - Left top rectangle area: $$2 \times 5 = 10$$ mm² - Left middle rectangle area: $$2 \times 4 = 8$$ mm² - Bottom left rectangle area: $$3 \times 5 = 15$$ mm² - Right rectangle area: $$8 \times 9 = 72$$ mm² - Top right triangle area: $$\frac{1}{2} \times 8 \times 5 = 20$$ mm² 5. **Sum areas of rectangles and subtract triangle area:** $$10 + 8 + 15 + 72 - 20 = 85$$ mm² 6. **Final answer:** The area of the figure is **85** square millimeters.