Chapter 4.2, Problem 7PPE

To determine

To represent: The relationship between the number of shapes and the perimeter using a table, words, an equation, and a graph.

Explanation of Solution

Calculation:

Perimeter of the figure refers to sum of all of its sides.

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

  

As each sides of the pentagon is equal to 1 unit,

Perimeter $=5=4(1)+1=4n+1$

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

  

As each sides of the pentagon is equal to 1 unit,

Perimeter $=9=4(2)+1=4n+1$

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

  

As each sides of the pentagon is equal to 1 unit,

Perimeter $=13=4(3)+1=4n+1$

From cases 1, 2 and 3, it can be observed that perimeter is equal to $4n+1$ where $n$ denotes number of pentagons.

Relationship using a Table

From cases 1, 2 and 3,

Number of pentagons	Perimeter
1	5
2	9
3	13
n	$4n+1$

Relationship using words

Perimeter is equal to $4n+1$ where $n$ denotes number of pentagons.

So,

Perimeter of a figure is equal to one more than four times the number of pentagons joined to form a figure.

Relationship using an equation

Perimeter is equal to $4n+1$ where $n$ denotes number of pentagons.

Let $y$ denotes perimeter and $x$ denotes number of pentagons connected.

So,

Equation is $y=4x+1$

Relationship using graph

To draw graph of the equation $y=4x+1$ , first find some points.

At $x=0,y=4(0)+1=1$

At $x=1,y=4(1)+1=5$

At $x=-1,y=4(-1)+1=-3$

At $x=2,y=4(2)+1=9$

At $x=-2,y=4(-2)+1=-7$

Plot points $(0,1),\left(1,5\right),\left(-1,-3\right),\left(2,9\right),\left(-2,-7\right)$