A circle is inscribed in a square. If the length of the diagonal of the square is $14\sqrt{2}\text{cm}$, what is the area (in sq cm) of the circle?

Let the side length of the square be $a$.The formula for the diagonal of a square is:
$$\text{Diagonal}=a\sqrt{2}$$
Given that the diagonal is $14\sqrt{2}\text{cm}$:
$$a\sqrt{2}=14\sqrt{2}⟹a=14\text{cm}$$
When a circle is inscribed inside a square, the diameter of the circle is equal to the side length of the square ($a$):
$$\text{Diameter}=14\text{cm}$$
$$\text{Radius }(r)=\frac{14}{2}=7\text{cm}$$
Now, calculate the area of the circle:
$$\text{Area}=\pi r^2=\frac{22}{7}\times 7\times 7=22\times 7=154{\text{cm}}^2$$