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The problem is asking to find the area of the shaded region within a square where two quarter circles intersect.

Given:
- Square \( ABCD \) with side length \( AB = BC = 42 \, \text{cm} \).
- The arcs \( \overarc{AD} \) and \( \overarc{BC} \) are quarter circles with radii equal to the side of the square.

### Steps to Solve:

1. **Area of the Square:**
   \[
   \text{Area of square} = s^2 = 42^2 = 1764 \, \text{cm}^2
   \]

2. **Area of Each Quarter Circle:**
   Since each quarter circle has a radius of 42 cm:
   \[
   \text{Area of one quarter circle} = \frac{1}{4} \times \pi \times r^2 = \frac{1}{4} \times \pi \times 42^2 = \frac{1}{4} \times \pi \times 1764 \, \text{cm}^2
   \]

3. **Area of the Overlapping Region (Lune Area):**
   The area of the overlapping region (the shaded region) is the area of the square minus the sum of the areas of the quarter circles:
   \[
   \text{Shaded Area} = \text{Area of square} - 2 \times \text{Area of one quarter circle}
   \]
   Plugging in the values:
   \[
   \text{Shaded Area} = 1764 - 2 \times \frac{1}{4} \times \pi \times 1764
   \]
   \[
   \text{Shaded Area} = 1764 - \frac{\pi \times 1764}{2}
   \]
   \[
   \text{Shaded Area} = 1764 \left(1 - \frac{\pi}{2}\right) \, \text{cm}^2
   \]
   Substituting \(\pi \approx 3.14\):
   \[
   \text{Shaded Area} = 1764 \times (1 - 1.57) \, \text{cm}^2
   \]
   \[
   \text{Shaded Area} = 1764 \times 0.215 \, \text{cm}^2
   \]
   \[
   \text{Shaded Area} \approx 379.26 \, \text{cm}^2
   \]

### Final Answer:
The area of the shaded region is approximately **379.26 cm²**.

Would you like more details on any specific step or have any questions?

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### Related Questions:

1. What is the area of the non-shaded region within the square?
2. How would the shaded area change if the side length of the square were doubled?
3. What would be the area of the shaded region if the arcs were semicircles instead of quarter circles?
4. How can you calculate the area of the shaded region using integration?
5. What is the significance of the overlapping area in other geometric contexts?

### Tip:
Always recheck your work by substituting back into the original formula to ensure accuracy.

Perhatikan gambar berikut. Jika panjang AB = BC = 42 cm, berapakah luas daerah yang diarsir?

Learn how to find the area of a shaded region formed by overlapping quarter circles within a square with a side length of 42 cm. This problem involves understanding the geometric properties of circles and squares, and applying area formulas for precise calculation.

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