The area of each square of a chessboard having 64 equal square is 8 sq. cm.  If there is a board around the board is 2 cm wide, then perimeter of the chessboard is:

16(1 + 4\(\sqrt {2}\)) cm

Area of one square on chessboard = 8 cm²

Area of the chessboard having 64 squares = 8 × 64 cm² 

Side of chessboard = \(\sqrt {8 × 64}\) cm = 16\(\sqrt {2}\) cm

Now including border of 2 m:

Side of bigger square = 16\(\sqrt {2}\) + 4

Perimeter = 4 × (16\(\sqrt {2}\) + 4) cm

              = 16 (4\(\sqrt {2}\) + 1) cm