perimeter patterns the university of texas at dallas

PERIMETER PERIMETER PATTERNSPATTERNS

The University of Texas at Dallas

PERIMETER PATTERNSPERIMETER PATTERNS• You will use a set of pattern pieces for this

activity.• Use the square to measure the sides of the other

pattern pieces. (The side of the square is 1 inch.)


1

1 1

1

11

1 1

1

1

1

1

11 1

11

1

1

1

1

11

2

PERIMETER PATTERNSPERIMETER PATTERNS• Use the squares to create a sequence.• Record your results in a table.


Number of squares 1 2 3 4 5 6

perimeter

1 + 1 + 1 + 1 = 4

Remember that perimeter is the sum of the sides

of a polygon

1 + 1 + 1 + 1 + 1 + 1 = 6

4 6

Complete the table!

PERIMETER PATTERNSPERIMETER PATTERNS• Complete your table to this one.


Number of squares 1 2 3 4 5 6

perimeter 4 6 8 10 12 14

• What is the perimeter if there are 20 squares in the figure?

Answer 42

PERIMETER PATTERNSPERIMETER PATTERNS• How did you figure out the perimeter?


Answer You may have built the figure or you may have extended the table using the pattern on the table. The perimeter goes up by 2 when a square is added.

• What is the perimeter if there are 100 squares in the figure?

Answer Although we can use the methods we used before, neither method is efficient.

PERIMETER PATTERNSPERIMETER PATTERNS• Let’s look for a pattern based on how

many squares are used in the sequence.

• We know that adding a square adds 2 to the perimeter.

• Think about that pattern.


PERIMETER PATTERNSPERIMETER PATTERNS• What does not change

regardless of the number of squares?


Answer

The 2 sides on each end

1 1

1 1

1 1

PERIMETER PATTERNSPERIMETER PATTERNS• How many sides of the

square counts besides the 2 on the ends?


Answer

For each square 2 sides are counted.

1

1

1 1

1 1

1 11

1 1 1

PERIMETER PATTERNSPERIMETER PATTERNS• If there are 100 squares in the figure, what

is the length of the sides?


1 2 3 98 99 100

………………………………..

100

• The perimeter of the figure with 100 squares is100 + 100 + 2 = 202

sides ends

PERIMETER PATTERNSPERIMETER PATTERNS• If there are 150 squares in the figure, what

is the perimeter?


Answer 150 + 150 + 2 = 302

• If there are any number of squares (n), what is the perimeter?

Answer n + n + 2 or 2n + 2

PERIMETER PATTERNSPERIMETER PATTERNS• Use your pattern pieces to create this

sequence and complete the table


Number of rhombuses 1 2 3 4 5 6

perimeter 4 6

PERIMETER PATTERNSPERIMETER PATTERNS• Does your table match this one?


Number of rhombuses 1 2 3 4 5 6

perimeter 4 6 8 10 12 14

PERIMETER PATTERNSPERIMETER PATTERNS• What is the perimeter of the figure with 30

rhombuses?


Answer 62

• What formula can be used to find the perimeter of a figure with “n” rhombuses?

Answer 2n + 2 or n + n + 2

This is the same pattern as the squares. The lengths of 2 sides of each rhombus plus 2 end segments gives the perimeter of any figure with any number of rhombuses

• Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of hexagons


Number of hexagons 1 2 3 4 5 6

perimeter 6 10

PERIMETER PATTERNSPERIMETER PATTERNS• Compare your table to this one


Number of hexagons 1 2 3 4 5 6

perimeter 6 10 14 18 22 26

PERIMETER PATTERNSPERIMETER PATTERNS• What pattern did you find to help you write

a formula?


Answer Adding a hexagon increases the perimeter by 4.

• What is the perimeter of the figure with 40 hexagons?

Answer 162

PERIMETER PATTERNSPERIMETER PATTERNS• What formula can be used to find the

perimeter of a figure with “n” hexagons?


Answer 4n + 2

This pattern is like the 2 previous ones in that there are 2 end segments, but each hexagon adds 4 segments to the sides

end

end

4 segments per hexagon + 2 end segments

• Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of triangles.


Number of triangles 1 2 3 4 5 6

perimeter 3 4



Number of triangles 1 2 3 4 5 6

perimeter 3 4 5 6 7 8

PERIMETER PATTERNSPERIMETER PATTERNS• How does the perimeter change when you

add another triangle?


Answer The perimeter of the figure increases by 1.

• What is the perimeter of a figure with 15 triangles?

Answer 17


perimeter of a figure with “n” triangles?


Answer n + 2

Only 1 side of each triangle adds to the perimeter of the figure plus 2 segments at the ends

end

end

1 side per triangle + 2 end segments

• Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of trapezoids.


Number of trapezoids 1 2 3 4 5 6

perimeter 5 8

Remember that the long side of the

trapezoid is 2 units

PERIMETER PATTERNSPERIMETER PATTERNS• Compare your table to this one?



perimeter 5 8 11 14 17 20

PERIMETER PATTERNSPERIMETER PATTERNS• How does the perimeter change when you

add a trapezoid?


Answer The perimeter of the figure increases by 3.

• What is the perimeter of a figure with 25 trapezoids?

Answer 77


perimeter of a figure with “n” trapezoids?


Answer 3n + 2

Each trapezoid adds 3 segments to the perimeter plus 2 segments at the ends.

end

end

3 segments per trapezoid + 2 end segments

• Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of parallelograms.


Number of parallelograms

3 6 8 12 15 18

perimeter 6



Number of parallelograms

3 6 9 12 15 18

perimeter 6 12 18 24 30 36

• Notice that to follow this pattern, you have to add 3 parallelograms at a time.

PERIMETER PATTERNSPERIMETER PATTERNS• Are there any other differences in this sequence?


Answer The pattern pieces do not share a side.

• What formula can be used to find the perimeter of a figure with “n” parallelograms?

Answer 2n

2 sides of each of the 3 parallelograms that makethe figure give us the perimeter of the parts of the sequence. Notice that there are no end segments with this pattern.

• Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of trapezoids.



perimeter




perimeter 6 10 14 18 22 26

PERIMETER PATTERNSPERIMETER PATTERNS• How many trapezoids do you add to create

the next figure?


Answer 2

• How does the perimeter change when you add 2 trapezoids?

Answer The perimeter increases by 4.

PERIMETER PATTERNSPERIMETER PATTERNS• How much does each trapezoid increase the perimeter?


Answer Two sides of each trapezoid increase the perimeter.

These 2 sides are used to find the perimeter.

PERIMETER PATTERNSPERIMETER PATTERNS


• What formula can be used to find the perimeter of a figure with “n” trapezoids?

Answer 2n + 2 2 sides for each trapezoid plus the 2 ends

end

end

perimeter patterns the university of texas at dallas

Documents