Question #41b40

1 Answer
CW
Apr 13, 2017

#16pi# sq. unit

Explanation:

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As shown in the figure, a regular hexagon can be divided into 6 congruent equilateral triangles, namely, #DeltaOAB, DeltaOBC# ... etc. #O# is the center of the circles and the hexagon.
Given side length #BC=8# units,
#=>OB=8#
radius of the circumscribed circle #r_1=OB=8#

In #DeltaOMB, angleBOM=30^@#,
#=> AM=8cos30=8*(sqrt3/2)=4sqrt3#
#=># radius of the inscribed circle #r_2=AM=4sqrt3#

#=># area of region between the two circles
#=pi(r_1^2-r_2^2)#
#=pi(8^2-(4sqrt3)^2)#
#=16pi# sq. unit

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