A parallelogram is cut by two sets of m paral | vedclass

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(C) parallelogram is formed by selecting two lines from each set of parallel lines.Initially,there are $2$ sides of the parallelogram. When $m$ lines

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$(^{m+2} C_2)^2$

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(C) parallelogram is formed by selecting two lines from each set of parallel lines.Initially,there are $2$ sides of the parallelogram. When $m$ lines are added parallel to each side,the total number of parallel lines in each set becomes $m + 2$.To form a parallelogram,we need to choose $2$ lines from the first set of $m + 2$ lines and $2$ lines from the second set of $m + 2$ lines.The number of ways to choose $2$ lines from the first set is $^{m+2}C_2$.The number of ways to choose $2$ lines from the second set is $^{m+2}C_2$.Therefore,the total number of parallelograms formed is $^{m+2}C_2 	imes ^{m+2}C_2 = (^{m+2}C_2)^2$.

$A$ parallelogram is cut by two sets of $m$ parallel lines,each set being parallel to one of its sides. How many parallelograms are formed in total?

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