Suppose in the plane 10 pair wise nonparallel lines intersect one another. What is the maximum possible number of polygons (with finite areas) that can be formed?

Step-by-step solution

Number of non-overlapping polygons =56-20=46 1 line divide plane into 2 regions 2 lines divide plane into 4 regions 3 lines divide plane into 7 regions 4 lines divide plane into 11 regions 5 lines divide plane into 16 regions 6 lines divide plane into 22 regions 7 lines divide plane into 29 regions 8 lines divide plane into 37 regions 9 lines divide plane into 46 regions 10 lines divide plane into 56 regions Now open regions for 3 lines are 6 Similarly for 10 lines are 20 Note : If we consider overlapping polygons