We can solve this by calculating the area of the square and subtracting the area of the inscribed circle. The area of the square is:
![Square=10\cdot10=100cm^2](https://img.qammunity.org/2023/formulas/mathematics/college/3o8ic9d25bs9upuu99zdy80g1pd9sxlt1x.png)
The formula for the area of a circle is:
![A=\pi r^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/lcgfavc89jro4qntamn2b9gfliomu1jwuf.png)
The radius of the inscribed circle is half the length of the side of the square, then, the radius is r = 5 cm
![Circle=\pi5^2=25\pi\text{ }cm^2](https://img.qammunity.org/2023/formulas/mathematics/college/xk55nolv4sv5u4xhbjj4mh0c279asclq0j.png)
Now, we rest:
![Square-Circle=100cm^2-25\pi cm^2\approx21.46cm^2](https://img.qammunity.org/2023/formulas/mathematics/college/jxb2i6ujmucrn0kvb32d869muj4gzba8nr.png)
The answer is 21.46cm²