What is the rule for the number of matchsticks for the pattern below if 'n' represents the number of squares ? ( 4 line segments in 1 square are considered as 4 matchsticks )
A boy found that four matchsticks are required to make a square, eight for two squares and so on. He was fascinated and developed a rule so as to calculate the number of matchsticks for any number of squares he needs to form. Calculate the number of matchsticks required for making 10 squares.
(a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: if you remove the vertical stick at the end, you will get a pattern of Cs.)
(b) The given figure gives a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.