To solve this problem, we need to find the side length of the chessboard given that each square has an area of 9 cm^2 and there is a margin of 3 cm around the board.

Let's break down the problem into smaller steps:

Step 1: Calculate the area of the chessboard
Since each square on the chessboard has an area of 9 cm^2, we can calculate the area of the entire chessboard by multiplying the number of squares on the board by 9.

The chessboard is an 8x8 grid, with a total of 64 squares. Therefore, the area of the chessboard is:
Area of chessboard = 64 squares * 9 cm^2/square = 576 cm^2

Step 2: Calculate the total area including the margin
To calculate the total area of the chessboard including the margin, we add the area of the margin to the area of the chessboard.

The margin is 3 cm wide on each side of the chessboard. Since the chessboard is a square, the total width including the margin is:
Total width = Width of chessboard + 2 * margin = 8 squares + 2 * 3 cm = 8 squares + 6 cm

Similarly, the total length including the margin is:
Total length = Length of chessboard + 2 * margin = 8 squares + 2 * 3 cm = 8 squares + 6 cm

Therefore, the total area including the margin is:
Total area = Total width * Total length = (8 squares + 6 cm) * (8 squares + 6 cm) = (8 squares + 6 cm)^2

Step 3: Find the side length of the chessboard
We are given that the total area including the margin is equal to 576 cm^2. So we can set up the equation:
Total area = (8 squares + 6 cm)^2 = 576 cm^2

Taking the square root of both sides, we get:
8 squares + 6 cm = √576 cm^2 = 24 cm

Subtracting 6 cm from both sides, we find:
8 squares = 24 cm - 6 cm = 18 cm

Finally, dividing both sides by 8, we find:
Side length of the chessboard = 18 cm / 8 = 2.25 cm

Since the side length of the chessboard is given in centimeters, we can round it to the nearest whole number, which is 2 cm.

Therefore, the correct answer is option D) 30 cm, as the closest whole number to the side length of the chessboard.