Question

Find the number of rectangles excluding squares from a rectangle of size $9\times 6$

Answer 1

Here $n=6$ and $p=9$

$\therefore$ No. of rectangles excluding square

$=\frac{6\cdot 9}{4}(6+1)(9+1)-\sum _{r=1}^6(7-r)(10-r)$

$=945-\sum _{r=1}^6(70-17r+r^2)$

$=945-154=791$