assumption :
It is a regular polygon and the body of mass 'm' moves with const speed 'v'
method:
angle made @ each corner = n-1/n * 180
wen it moves along 1 side the mom is mv=p...
now this mv is brought to 0 and 'mv' is provided along another side...so impulse experienced is the addn of 2 vectors of mag mv wid an angle of n-1/n * 180 between them
=
rt( p^2 + p^2 + 2p^2cos(n-1/n *180))