Question

Suppose in the plane 10 pairwise non-parallel lines intersect one another. What is the maximum possible number of polygons (with finite areas) that can be formed?

Answer 1

If we consider the case.

In given figure there are 3 polygon in all. But if we count non-overlapping polygons then it is 2.

If we consider non-overlapping, then the solution is as follows :

Total number of regions in which 10 lines divide to

of which exactly 20 are open (unbounded)

∴ Polygons = 56 – 20 = 36