1. **State the problem:** We need to find the perimeter of the given irregular polygon with sides labeled 30 mm, 15 mm, 20 mm, and 40 mm, plus the slanting right side. 2. **Identify all sides:** The polygon has the following sides: - Top horizontal side = 30 mm - Left vertical side = 15 mm - Inner horizontal segment = 20 mm - Bottom horizontal side = 40 mm - Right slanting side = unknown length 3. **Find the length of the right slanting side:** Since the polygon is irregular, we use the Pythagorean theorem to find the slanting side. The vertical difference is $15$ mm (left side) minus the vertical height of the inner segment (assumed 0 since no vertical info given), so vertical leg = $15$ mm. The horizontal difference is $40 - 30 = 10$ mm. Using Pythagoras: $$\text{slant} = \sqrt{15^2 + 10^2} = \sqrt{225 + 100} = \sqrt{325}$$ 4. **Calculate the slant length:** $$\sqrt{325} = 5\sqrt{13} \approx 18.03$$ 5. **Calculate the perimeter:** Sum all sides: $$30 + 15 + 20 + 40 + 18.03 = 123.03$$ 6. **Round to nearest whole number:** $$\boxed{123}$$ Thus, the perimeter of the figure is approximately 123 mm.