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

Area of the regular polygon

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

Area Square meter

Cost of carpeting Rupees