Final answer:
To find the number of rectangles on an 8×8 chessboard, calculate the combinations of selecting two lines from nine possible horizontal and vertical lines. Multiply the two results together which is 36 × 36 to get 1296 rectangles.
Step-by-step explanation:
The question asks how many rectangles are there on an 8×8 chessboard, not just the squares. To determine the number of rectangles, we can use a formula that involves calculating the number of ways to select two horizontal sides and two vertical sides on the chessboard to form the rectangle. For an 8×8 chessboard, we have 9 lines that we can choose as the sides of the rectangles, both horizontally and vertically (since the sides of the rectangles are determined by the lines between the squares, plus one line at the edge outside of the square).
To calculate the total number of rectangles, use the combination formula for both horizontal (H) and vertical (V): H = 9 choose 2, V = 9 choose 2. Calculating each, we have H = V = (9×8)/2 = 36. Since the rectangles are independent in terms of their vertical and horizontal sides, multiply H by V: 36 × 36 = 1296.
Therefore, the total number of rectangles on an 8×8 chessboard is 1296.