To find the area of a regular quadrilateral inscribed in a circle with a radius of 8√2, we need to break down the steps:
1. **Understand the Properties of a Regular Quadrilateral:** A regular quadrilateral is a square, which means it has all sides equal in length and all angles equal to 90 degrees.
2. **Determine the Side Length of the Quadrilateral:** Since the quadrilateral is inscribed in a circle with a radius of 8√2, the diagonal of the square is equal to the diameter of the circle, which is twice the radius. So, the side length of the square is the diagonal divided by √2, giving us 8√2 / √2 = 8.
3. **Calculate the Area of the Square:** The area of a square is side length squared. So, for a square with a side length of 8, the area would be 8 * 8 = 64 square units.
Therefore, the area of the regular quadrilateral inscribed in a circle with a radius of 8√2 is 64 square units.
