1. **Problem statement:** We have a square of side length 15 cm with 4 identical quarter circles drawn inside it, one in each corner. The shaded part is the region inside the square bounded by the arcs of these quarter circles. We need to find the perimeter of this shaded part. 2. **Understanding the figure:** Each quarter circle has radius equal to the side of the square, which is 15 cm. 3. **Perimeter of the shaded part:** The shaded part is bounded by the arcs of the 4 quarter circles. Each quarter circle arc length is given by the formula for arc length of a circle segment: $$\text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi r$$ where $\theta = 90^\circ$ for a quarter circle, and $r = 15$ cm. 4. Calculate the arc length of one quarter circle: $$\text{Arc length} = \frac{90}{360} \times 2 \times 3.14 \times 15 = \frac{1}{4} \times 2 \times 3.14 \times 15 = \frac{1}{2} \times 3.14 \times 15 = 1.57 \times 15 = 23.55 \text{ cm}$$ 5. Since the shaded part's perimeter consists of 4 such quarter circle arcs, the total perimeter is: $$4 \times 23.55 = 94.2 \text{ cm}$$ **Final answer:** The perimeter of the shaded part is $94.2$ cm.