if there is a polygon of n sides each having resistors r connected in series.what will the total resistance across any diagonal

If the number of resistors are n = side of polynomial.

Thus if a diagonal devides the polynomial into two polynomials, one having N+1 sides and the other having n-N+1 sides (with the diagonal itself acting as one side, there will be two sets of series connection of resistaces being connected in parallel having NR and (n-N)R resistances.

Thus the total resistance will be the total sum of parallle connection of these resistances.