To solve the problem, follow these steps:

Step 1: Use the area of the circle to find (r^2)

The area of a circle is given by (A = \pi r^2). We know the area is (2\pi):
[ \pi r^2 = 2\pi ]
Divide both sides by (\pi):
[ r^2 = 2 ]

Step 2: Calculate the area of the square

The side length of the square equals the radius of the circle ((s = r)). The area of the square is (s^2):
[ \text{Area of square} = s^2 = r^2 = 2 ]

Answer: (\boxed{2})

作者声明:本文包含人工智能生成内容。