Question 1153292: Determine the area of the regular octagon circumscribing a circle having an area of 126 m2.
A. 127.83 m2
B. 132.90 m2
C. 119.05 m2
D. 113.44 m2
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Draw this
The area of the circle is 126 m^2=pi*r^2
therefore, r=6.333
Each of the 8 parts of the octagon is a triangle with central angle 45 deg
Draw a perpendicular to the side, and this bisects the central angle.
That triangle has angle 22.5, the opposite side is half the length of a side of the octagon, and the perpendicular line is the adjacent side.
cos22.5=adj/6.333; adj side =5.851
sin 22.5=opp/6.333, opp side=2.424
the side of the octagon is 4.848, double the above for sin 22.5
the altitude is 5.851
1/2 that product is the area of the triangle.
There are 8 such triangles, so 4 times the product is the answer or 113.46 m^2.
D.
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