how many rectangles are there in this figure........please get me the answer very soon as possible

Hello student,
Please find the answer to your question below
Ans: There are 70 pure rectangles, exclusive of squares in a 4 x 4 grid.
i) In a 4 x 4 grid, there are 5 parallel lines across and 5 parallel lines vertical.
To form a parallelogram we need any 2 from either set.
The selection of them is: C(5,2) x C(5,2) = 10 x 10 = 100
[This 100 inclusive of pure rectangles and squares]
ii) The number of squares:
Taking full panel, 1 x 1 = 1
Taking any 3 lines from across as well vertical, we can form 2 from either direction
==> 2 x 2 = 4 squares.
Taking any 2 lines in either direction,
the number of squares can be formed = 3 x 3 = 9
Finally 4X4 = 16 squares
So total number of squares = 1 + 4 + 9 + 16 = 30
Thus number of pure rectangles = 100 - 30 = 70