Chapter 4.2, Problem 18PPE

To determine

To calculate: Perimeter of the figure if 1 more octagon is added.

Answer to Problem 18PPE

The perimeter of the figure is 29 units if 1 more octagon is added

Explanation of Solution

Calculation:

Perimeter of a figure is equal to the sum of all of its sides.

Now find the perimeter of each of the given octagons.

Case 1: If number of octagons $(n)$ is 1

  

As each of the sides equal to 1 unit,

Perimeter of one octagon $=8=7(1)+1=7(n)+1$ units

Case 2: If number of octagons $(n)$ is 2

  

As each of the sides equal to 1 unit,

Perimeter of two octagons $=15=7(2)+1=7(n)+1$ units

Case 3: If number of octagons $(n)$ is 3

  

As each of the sides equal to 1 unit,

Perimeter of three octagons $=22=7(3)+1=7(n)+1$ units

From cases 1, 2 and 3, it can be observed that perimeter is equal to $7n+1$ where $n$ denotes number of octagons.

To find perimeter of the figure if 1 more octagon is added, put $n=4$ in $7n+1$

So,

Perimeter of the figure $=7n+1=7(4)+1=29$ units