Question 1106939
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When a regular hexagon is inscribed in a circle, the side length of the hexagon is equal to the radius of the circle.<br>
Viewing the regular hexagon as six equilateral triangles, the apothem of the hexagon is the altitude of an equilateral triangle with side length 12; the length of the apothem is (sqrt(3)/2) times the length of the side.<br>
A: the length of the apothem is {{{6*sqrt(3)}}} which is (to 2 decimal places) 10.39.<br>
The area of the hexagon is the area of the 6 equilateral triangles.  The area of an equilateral triangle wiht side length s is {{{(s^2*sqrt(3))/4}}}.
B: The area of the hexagon is {{{6*((12^2*sqrt(3))/4) = 216*sqrt(3)}}} which is (to the nearest whole number) 374.