To find the area of a regular hexagon inscribed in a circle with a radius of 32√3, you can follow these steps:
1. Divide the regular hexagon into 6 equilateral triangles. Each of these triangles will have a central angle of 60 degrees in the circle.
2. The radius of the circle is 32√3. This means the side length of the equilateral triangle (which is also the radius of the circle) is 32√3.
3. Calculate the area of one of the equilateral triangles. The formula for the area of an equilateral triangle is A = (side length^2 * √3) / 4.
4. Substitute the side length of 32√3 into the formula to find the area of one equilateral triangle.
5. Since there are 6 equilateral triangles in a regular hexagon, multiply the area of one equilateral triangle by 6 to find the total area of the regular hexagon.
6. By following these steps, you can accurately determine the area of the regular hexagon inscribed in the given circle.
