Number of rectangles possible is

= (Number of ways to choose a horizontal side of odd length).(Number of ways to choose a vertical side of odd length)

$\left(1+3+5+\text{.....}+\left(2\text{m}-1\right)\right)\left(1+3+5+\text{.....}+\left(2n-1\right)\right)={\text{m}}^2{n}^2$