SOLUTION: A regular octagon is inscribed in a circle of radius 10.0 centimeters. Approximate the perimeter of the octagon. (Round your answer to the nearest tenth.)

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Question 656492: A regular octagon is inscribed in a circle of radius 10.0 centimeters. Approximate the perimeter of the octagon. (Round your answer to the nearest tenth.)
Answer by MathDazed(34) (Show Source):
You can put this solution on YOUR website!
For this question you have to think about a few things.
If its a regular octagon then all sides and angles are conguent or equal. You can also find the sum of interior angles of the octagon using the formula 180(n-2) where n is the number of side....Hence the sum of the interior angles are 180(8-2) = 180*6 = 1080. Divide 1080/8 and you'll get each interior angle 135
Now you can also think of the octagon having 8 equal triangles in it. The angles of the vertex of the triagles which would be at the center of the circle all equal to 45 (360/8).
So lets work with the triangle only. It's an isoceles triangle with side 10(the radius) and the angle between these side is 45 degrees. If it's an isoceles then the other angles are 67.5 degrees...(180-45)/2. Divide your triangle in half so you can find half of the base (which would be a side of your octagon). We can use cos 67.5 = adj/10 = 3.8268. Now you times this by 2 to get the side of the octagon, 7.65. Hence the perimeter is 7.65*8 = 61.2cm
Pweeeeh! I hope this helps!!!