Question

Number of rectangles in the grid shown which are not squares is

• A. $160$
• B. $162$
• C. $170$
• D. $185$

Answer 1

The correct option is C $170$

To find number of rectangle

number of rectangle $=(\frac{m+1}{2}{)}^m\times (\frac{(n+1)}{2}{)}^n$

$=\frac{5}{2}\times \frac{7}{2}\times 4\times 6$

$=210$

Number of square $=n\times m+(n-1)(m-1)+(n-2)(m-2)+(n-3)(m-3)$

$=6\times 4+5\times 3+4\times 2+3\times 1$

$=40$

Number of rectangle with square $=210-40=170$