Polygon

If a circle is inscribed in a polygon ... then each angle between the diagonals meeting at the centre of the circle is 2∩/n radian...

The rad of circle given is r ...

Perimeter of circle is 2p = 2∩r .. r = p/∩ ...

On proceeding like this, ... the expr. comes out to be ...

length of half-diagonal of the polygon = h = r cos ∩/n
=p/∩ cos ∩/n

if n is large [ polygon ] .. therefore cos ∩/n is small

cos ∩/n can be approximated as ∩/n

Hence .. h = p/∩ * ∩/n = p/n

On further calculation ...

Hence area of the polygon = 2∩/n * p/∩ (p√(∩²-n²)n∩ )

= 2p²âˆš(∩²-n²)∩n²

Hope there r no calculation mistakes ..... sorry if there r any !!!

sorry...the perimeter of the polygon is 2p...you went on it right.

I've figured it out,thanks....