1. **Problem statement:** Find the perimeter of the shaded region in the first shape, which is a quarter circle inside a square with side length 20 cm. 2. **Understanding the shape:** The square has sides of length 20 cm. The quarter circle is drawn inside the square, touching two adjacent sides. 3. **Formula for perimeter of shaded region:** The perimeter consists of two sides of the square plus the arc length of the quarter circle. 4. **Calculate the arc length:** The radius $r$ of the quarter circle equals the side of the square, $r=20$ cm. The circumference of a full circle is $$C=2\pi r=2\pi \times 20=40\pi.$$ The quarter circle arc length is $$\frac{1}{4} \times 40\pi = 10\pi.$$ 5. **Calculate the total perimeter:** The perimeter $P$ is the sum of two sides of the square plus the quarter circle arc: $$P = 20 + 20 + 10\pi = 40 + 10\pi.$$ 6. **Final answer:** The perimeter of the shaded region is $$\boxed{40 + 10\pi \text{ cm}}.$$