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Area of a Regular polygon of n sides when the radius r of the circumscribed circle is given:
Let  be the radius of the circumscribed circle.
 Area of the polygon  area of 
But Area of  
Also, Perimeter of the polygon 
But 
 
Also 
 
 
 Perimeter 
Or  (As )
 
Example:
A regular decagon is inscribed in a circle, the radius of which is . Find the area of the decagon.
Solution:
Here  , 
Area of decagon 
 Square cm
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