a parallelogram is cut by two sets of m parallel lines to its sides. find the no. of parallelograms formed..

Dear ajinkya

parallelogram is cut by two sets of m parallel lines to its sides.

then we have  2 sets of (m+2) parallel lines ( 2 lines of the parallelogram)

so parallelogram is formed by taking 2 lines from each set

 = ^m+2C₂ * ^m+2C₂

 = [(m+2)(m+1)/2 ]²

 this also include 1 original parallelogram

 so total number of new parallelogram formed is  =   [(m+2)(m+1)/2 ]²   -1