1. **State the problem:** Find the area of the given irregular polygon with labeled side lengths in millimeters. 2. **Approach:** We can divide the polygon into simpler shapes (rectangles and triangles), calculate their areas, and sum them. 3. **Identify shapes:** - The polygon can be split into a large rectangle on the left and a smaller rectangle plus a triangle on the right. 4. **Calculate the large rectangle area:** - Height = 15 mm - Width = 11 mm - Area = $15 \times 11 = 165$ mm$^2$ 5. **Calculate the small rectangle area on the bottom right:** - Height = 2 mm (small vertical segment) - Width = 3 mm (adjacent horizontal segment) - Area = $2 \times 3 = 6$ mm$^2$ 6. **Calculate the triangle area on the top right:** - Base = 7 mm (diagonal side) - Height = 4 mm (small vertical segment near top right) - Area = $\frac{1}{2} \times 7 \times 4 = 14$ mm$^2$ 7. **Sum all areas:** $$165 + 6 + 14 = 185$$ mm$^2$ 8. **Final answer:** The area of the polygon is **185** square millimeters.