What is the area of the shaded region? What is the answer to the nearest tenth of a square unit?

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1 Answer
May 25, 2017

34.75square units

Explanation:

Where theta=360/"number of sides"=360/6=60^@

Radius of Circle
r=sqrt(s^2/(2-2costheta))
r=sqrt(8^2/(2-2cos60^@))
r=sqrt(64/(2-2(1/2)))=sqrt(64)=8

Thus the radius is also 8.

Area of Hexagon:
A=("number of sides")((r^2sintheta)/2)
A=(6)((8^2sin60^@)/2)=192sqrt(3)

Area of Circle:
A=pir^2=64pi

Area of Shaded Region:
("Area of Circle")-("Area of Hexagon")=64pi-96sqrt(3)/2=34.75square units