To calculate the area of the shaded region in the given diagram:

1. Understand the geometry: The figure is a square with side length $10 \, \text{cm}$, and the arcs are segments of circles with radii equal to the side length of the square. These arcs represent portions of a quarter-circle, where the circle's radius equals $10 \, \text{cm}$.

2. Calculate the area of the square: $\text{Area of square} = \text{side}^2 = 10^2 = 100 \, \text{cm}^2$

3. Calculate the total area of the quarter-circle arcs: Each quarter-circle has an area of: $\text{Area of one quarter-circle} = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (10)^2 = 25\pi \, \text{cm}^2$ There are two such quarter-circle arcs, so the total area of the circular regions is: $2 \times 25\pi = 50\pi \, \text{cm}^2$

4. Calculate the area of the shaded region: The shaded region is the area of the square minus the total area of the circular regions: $\text{Shaded area} = \text{Area of square} - \text{Area of circular regions}$ Substituting the values: $\text{Shaded area} = 100 - 50\pi \, \text{cm}^2$ Approximating $\pi \approx 3.14$:

   $$$$

The shaded area is calculated as follows:

1. Area of the square: The square has a side length of $10 \, \text{cm}$, so: [ \text{Area of square} = 10^2 = 100 , \text{cm}^2$$

2. Area of the circular segments: There are two quarter-circles, each with a radius of $10 \, \text{cm}$. The area of one quarter-circle is: $\frac{1}{4} \pi r^2 = \frac{1}{4} \pi (10)^2 = 25\pi \, \text{cm}^2$ The total area of the two quarter-circles is: $2 \times 25\pi = 50\pi \, \text{cm}^2$

3. Area of the shaded region: The shaded area is the area of the square minus the total area of the two quarter-circles: $\text{Shaded area} = 100 - 50\pi \, \text{cm}^2$

   Substituting $\pi \approx 3.14$: $\text{Shaded area} \approx 100 - 50(3.14) = 100 - 157 = -57 \, \text{cm}^2$

Therefore, the shaded area is approximately $-57 \, \text{cm}^2$.