Regular hexagon ABCDEF is inscribed in a circle P with a radius of 12 centimeters. Calculate the exact areas of circle P and regular hexagon ABCDEF. Find the exact area of the shaded region shown in t

Regular hexagon ABCDEF is inscribed in a circle P with a radius of 12 centimeters. Calculate the exact areas of circle P and regular hexagon ABCDEF. Find the exact area of the shaded region shown in the image above. Imagine circle P with regular inscribed octagon ABCDEFGH, rather than regular hexagon ABCDEF. In two or more complete sentences, describe the effect the number of sides of the polygon would have on the area of the shaded region.