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Area of a Regular polygon of n sides when the radius r of the inscribed circle is given:
Since 
 Area of the polygon  area of the 
But  , 
  and 
Hence, area of the regular polygon 
Also, perimeter of the polygon 
 (Putting for  from above)
 
Example:
A regular octagon circumscribed a circle of  radius. Find the area of the octagon.
Solution:
Here  , 
 Area of the polygon 
 Square meter approx.
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