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PERIMETER PATTERNS

Dive into patterns using square, rhombus, hexagon, and triangle pieces to explore perimeter formulas and sequences. Learn to calculate perimeters efficiently and identify patterns in geometric figures with varying shapes and numbers of sides.

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PERIMETER PATTERNS

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  1. PERIMETER PATTERNS The University of Texas at Dallas

  2. PERIMETER 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 The University of Texas at Dallas

  3. PERIMETER PATTERNS • Use the squares to create a sequence. • Record your results in a table. 4 6 Remember that perimeter is the sum of the sides of a polygon 1 + 1 + 1 + 1 = 4 1 + 1 + 1 + 1 + 1 + 1 = 6 Complete the table! The University of Texas at Dallas

  4. PERIMETER PATTERNS • Complete your table to this one. • What is the perimeter if there are 20 squares in the figure? Answer 42 The University of Texas at Dallas

  5. PERIMETER 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. The University of Texas at Dallas

  6. PERIMETER 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. The University of Texas at Dallas

  7. PERIMETER PATTERNS • What does not change regardless of the number of squares? 1 1 1 1 Answer The 2 sides on each end 1 1 The University of Texas at Dallas

  8. PERIMETER PATTERNS 1 • How many sides of the square counts besides the 2 on the ends? 1 Answer 1 1 For each square 2 sides are counted. 1 1 1 1 1 1 1 1 The University of Texas at Dallas

  9. PERIMETER 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 is 100 + 100 + 2 = 202 sides ends The University of Texas at Dallas

  10. PERIMETER 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 The University of Texas at Dallas

  11. PERIMETER PATTERNS • Use your pattern pieces to create this sequence and complete the table The University of Texas at Dallas

  12. PERIMETER PATTERNS • Does your table match this one? The University of Texas at Dallas

  13. PERIMETER 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 The University of Texas at Dallas

  14. Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of hexagons The University of Texas at Dallas

  15. PERIMETER PATTERNS • Compare your table to this one The University of Texas at Dallas

  16. PERIMETER 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 The University of Texas at Dallas

  17. PERIMETER 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 The University of Texas at Dallas

  18. Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of triangles. The University of Texas at Dallas

  19. PERIMETER PATTERNS • Does your table match this one? The University of Texas at Dallas

  20. PERIMETER 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 The University of Texas at Dallas

  21. PERIMETER PATTERNS • What formula can be used to find the 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 The University of Texas at Dallas

  22. Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of trapezoids. Remember that the long side of the trapezoid is 2 units The University of Texas at Dallas

  23. PERIMETER PATTERNS • Compare your table to this one? The University of Texas at Dallas

  24. PERIMETER 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 The University of Texas at Dallas

  25. PERIMETER PATTERNS • What formula can be used to find the 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 The University of Texas at Dallas

  26. Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of parallelograms. The University of Texas at Dallas

  27. PERIMETER PATTERNS • Does your table match this one? • Notice that to follow this pattern, you have to add 3 parallelograms at a time. The University of Texas at Dallas

  28. PERIMETER 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 make the figure give us the perimeter of the parts of the sequence. Notice that there are no end segments with this pattern. The University of Texas at Dallas

  29. Create a table for this sequence and write a formula for finding the perimeter of a figure with any number of trapezoids. The University of Texas at Dallas

  30. PERIMETER PATTERNS • Does your table match this one? The University of Texas at Dallas

  31. PERIMETER 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. The University of Texas at Dallas

  32. PERIMETER 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. The University of Texas at Dallas

  33. PERIMETER PATTERNS • What formula can be used to find the perimeter of a figure with “n” trapezoids? Answer 2 sides for each trapezoid plus the 2 ends 2n + 2 end end The University of Texas at Dallas

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