1. **State the problem:** Find the area of the given polygon with specified side lengths. 2. **Analyze the figure:** The polygon is a stepped shape with vertical and horizontal edges. We can divide it into rectangles and sum their areas. 3. **Identify rectangles:** - Left rectangle: height $15$ mm, width $3$ mm - Middle upper rectangle: height $5$ mm, width $3$ mm - Middle lower rectangle: height $3$ mm, width $3$ mm - Bottom rectangle: height $3$ mm, width $4$ mm - Right rectangle: height $8$ mm, width $4$ mm (since bottom edge is $4$ mm) 4. **Calculate areas:** - Left rectangle area: $15 \times 3 = 45$ mm$^2$ - Middle upper rectangle area: $5 \times 3 = 15$ mm$^2$ - Middle lower rectangle area: $3 \times 3 = 9$ mm$^2$ - Bottom rectangle area: $3 \times 4 = 12$ mm$^2$ - Right rectangle area: $8 \times 4 = 32$ mm$^2$ 5. **Sum all areas:** $$45 + 15 + 9 + 12 + 32 = 113$$ 6. **Final answer:** The area of the figure is $113$ square millimeters.