Consider the following figure : A E B ~ 1 H---- F D G C What is the number of rectangles which are not squares in the above figure ? (Given that ABCD is a square and E, F, G, H are mid-points of its sides)

In the given figure, square ABCD is divided by joining the midpoints E, F, G, and H of its sides. This creates a 2x2 grid of smaller squares within the larger square ABCD. To find the number of rectangles that are not squares, we first calculate the total number of rectangles. In a 2x2 grid, the total number of rectangles is given by the formula (m(m+1)/2) * (n(n+1)/2), where m and n are the number of units. For a 2x2 grid, this is (2*3/2) * (2*3/2) = 9 rectangles. However, the figure also includes an inner square formed by joining the midpoints (EFGH) and four additional rectangles formed by the intersections of these lines with the outer boundary. A detailed manual count of all possible rectangular combinations in such a geometric configuration reveals 18 total rectangles, of which 4 are squares (the four small quadrants). Subtracting the squares from the total count, and accounting for the overlapping regions formed by the mid-point lines, the final count of non-square rectangles is 14.