Question

Suppose you know the perimeter of n octagons arranged as shown. What would you do to find the perimeter if 1 more octagon was added?

Answer 1

As shown in the figures given :

For Figure 1 : perimeter = 8 units   [As can be seen in the figure]

For figure 2(with 2 octagons) : perimeter = 8 × 2 - 1 = 15 units    [since 1 side is common ]

For figure 2(with 3 octagons) : perimeter = 8 × 3 - 2 = 22 units  [since 2 sides is common ]

If one more octagon is added

then perimeter = 8 × 4 - 3 = 29 units    [since 3 sides will be common ]