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Let , be the length of a side of a regular polygon of  sides and  be the center of the polygon.
As there are sides,  similar triangles are formed.
Let  be one of the  triangles, then
 and 
 Area of the regular polygon  area of 
But  , 
Or 
Or 
 Area of the regular polygon 
Also, perimeter of the polygon 
 
Example:
Find the cost of carpeting an octant floor with sides measuring , if the carpet costs Rs.  per square meter.
Solution:
Here  , 
 Area 
 Square meter
 Square Meter Approximate.
 Cost of carpeting  Rupees
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