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 of the circle?

1. Let the side 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 ($a$):
$$\text{Diameter }(d)=14\text{ cm}$$
$$\text{Radius }(r)=\frac{d}{2}=\frac{14}{2}=7\text{ cm}$$
Calculate the area of the circle:
$$\text{Area}=\pi r^2=\frac{22}{7}\times 7\times 7=22\times 7=154{\text{ cm}}^2$$