Four horizontal lines and four vertical lines are drawn in a plane. In how many ways can four lines be chosen such that a rectangular region is enclosed?
Four vertical lines and four horizontal lines enclose a 3 x 3 rectangle. How many separate rectangles of all sizes are there?
Individually, there will be
9 1 x 1 rectangles (1 space down and 1 space across)
6 1 x 2 rectangles (1 space down and 2 spaces across)
6 2 x 1 rectangles
3 1 x 3 rectangles
3 3 x 1 rectangles
4 2 x 2 rectangles.
2 2 x 3 rectangles
2 3 x 2 rectangles
1 3 x 3 rectangles
Total: 36 rectangles.
Four vertical lines and four horizontal lines enclose a 3 x 3 rectangle. How many separate rectangles of all sizes are there?
Individually, there will be
9 1 x 1 rectangles (1 space down and 1 space across)
6 1 x 2 rectangles (1 space down and 2 spaces across)
6 2 x 1 rectangles
3 1 x 3 rectangles
3 3 x 1 rectangles
4 2 x 2 rectangles.
2 2 x 3 rectangles
2 3 x 2 rectangles
1 3 x 3 rectangles
Total: 36 rectangles.