**Question: **There is a grid of 20 squares by 10 squares. How many different rectangles are possible?

Note that square is a rectangle.

**Answer:**

11550

The Generic solution to this is:

Total number of rectangles = (Summation of row numbers) * (Summation of column numbers)

Here there are 20 rows and 10 columns or vice versa. Hence, total possible rectangles

= ( 20 + 19 + 18 + 17 + 16 + .... + 3 + 2 + 1 ) * ( 10 + 9 +8 + 7 + .... + 3 + 2 + 1)

= ( 210 ) * (55)

= 11550

Hence, total 11,550 different rectangles are possible.

If you don't believe it, try formula on some smaller grids like 4x2, 3x2, 3x3 etc...