SOLUTION: What is the area of the region between a regular hexagon with sides of 6" and its inscribed circle. Please show work

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Question 304048: What is the area of the region between a regular hexagon with sides of 6" and its inscribed circle.
Please show work

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The area of hexagon = 3sqrt3 * r^2
r- length of side
area = 3 sqrt3/2 *6^2
= 54sqrt3
Area of circle = pi*r^2
pi*6^2
= 36p
Difference = 36*pi-54*sqrt3
= 19.56 sq. inches is the area of the region