SOLUTION: A hexagon of side length 4cm has both an inscribed and a circumscribed circle. What is the area of the region (called an annulus) between the two circles?

Algebra ->  Surface-area -> SOLUTION: A hexagon of side length 4cm has both an inscribed and a circumscribed circle. What is the area of the region (called an annulus) between the two circles?      Log On


   



Question 1179701: A hexagon of side length 4cm has both an inscribed and
a circumscribed circle. What is the area of the
region (called an annulus) between the two circles?

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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The radius of the circumscribed circle is 4 cm  ---- the same as the side length of the hexagon.



The radius of the inscribed circle is  4%2A%28sqrt%283%29%2F2%29 cm  --- the same as the apothem of the regular hexagon.



Therefore, the area under the problem's question is


    area = pi%2A16 - pi%2A16%2A%283%2F4%29 = 4pi  square centimeters.    ANSWER

Solved, answered and explained.