Question

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.

Answer 1

not seeing your "shaded area" assuming it is not either the whole circle, or the hexagon. so perhaps the area of the circle that is not the hexagon circle area = pi * r^2 = 3.14*12^2 = 3.14*144 = 452.389 hexagon area = (3*sqrt(3))/2 * r ^2 = 216 * sqrt(3) = 374.123 difference (if that is what you need) = 78

Answer 2

the greater the number of sides of an inscribed shape, the closer it is to having the same area as the circle

Answer 3

Thank you for replying (: