Chapter 4.2, Problem 6PPE

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 hexagons $(n)$ is 1

  

As each sides of the hexagonare equal to 1 unit,

Perimeter $=6=5(1)+1=5n+1$

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

  

As each sides of the hexagonare equal to 1 unit,

Perimeter $=11=5(2)+1=5n+1$

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

  

As each sides of the hexagonare equal to 1 unit,

Perimeter $=16=5(3)+1=5n+1$

From cases 1, 2 and 3, it can be observed that perimeter is equal to $5n+1$ where $n$ denotes number of hexagons.

Relationship using a Table

From cases 1, 2 and 3,

Number of hexagons	Perimeter
1	6
2	11
3	16
n	$5n+1$

Relationship using words

Perimeter is equal to $5n+1$ where $n$ denotes number of hexagons.

So,

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

Relationship using an equation

Perimeter is equal to $5n+1$ where $n$ denotes number of hexagons.

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

So,

Equation is $y=5x+1$

Relationship using graph

To draw graph of the equation $y=5x+1$ , first find some points.

At $x=0,y=5(0)+1=1$

At $x=1,y=5(1)+1=6$

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

At $x=2,y=5(2)+1=11$

At $x=-2,y=5(-2)+1=-9$

Plot points $(0,1),\left(1,6\right),\left(-1,-4\right),\left(2,11\right),\left(-2,-9\right)$