Question

In the following figures, polygons are formed by increasing the number of sides using matchsticks as given below.
Find the number of sticks required to form the next shape by tabulation and generalisation.

• A. 9
• B. 8
• C. 12
• D. 10

Answer 1

The correct option is B 8

In the above pattern of polygons, in the first shape ( x = 1), we get a closed shape called a triangle.
Similarly the second shape ( x = 2 ) gives a four sided polygon and the third shape ( x = 3) is a five sided polygon and continuing in the same way two more shapes are formed.
If the number of match sticks required to form each of the shapes is taken as y, then the values of x and y are tabulated as given below.

x	1	2	3	4	5	....
y	3	4	5	6	7	....

when x = 1, y = 3 = 1+2
when x = 2 , y = 4 = 2+2
when x = 3, y = 5 = 3+2
when x = 4 , y = 6 = 4+2
when x = 5, y = 7 = 5+2
Hence, each of the values of y which we get from the table is 2 more than x. That is y = x + 2 .
Therefore, 6th shape (x=6) will have y = 8 = 6 + 2 (8 match sticks)