Step 1. We need to find the maximum area of a rectangle inscribed in a circle.
The diameter of the circle is:

Step 2. The radius of the circle is:

Step 3. The formula to find the maximum area of a rectangle inscribed in a circle with radius r is:

Step 4. Substituting the known value of r and finding the area:

The maximum area is 32cm^2.
Step 5. The maximum area of a rectangle or quadrilateral inside a circle happens when the sides of the quadrilateral are equal. This means the quadrilateral is a square.
For a square the area formula is:

Where l is the length.
Step 6. Substituting the area to find the length of the sides:

Thus, the dimensions are:

Answer: The figure for which the area is maximum is the square, and the dimensions are:
![4√(2c)m*4\sqrt[]{2}cm](https://img.qammunity.org/2023/formulas/mathematics/college/sx41oeue8z70a1xjf4sjppz9x3trko0dvp.png)