Section B Practice Problems

Problem 1

Find the perimeter of each figure.

a
8-sided shape on dot grid.

b
8-sided shape with perimeter marked with tick marks.

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Solution
  1. 20 units. Sample response: 2+1+1+3+1+3+2+7=202 + 1 + 1 + 3 + 1 + 3 + 2 + 7 =20 
  2. 18 units. Sample response: 4+4+3+2+2+1+1+1=184 + 4 + 3 + 2 + 2 + 1 + 1 + 1 = 18

Problem 2

  1. Draw 2 different shapes with a perimeter of 20 units.

    Dot grid.

  2. What strategy did you use to draw your shapes?

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Solution
  1. Sample responses: 5 unit by 5 unit square and 9 unit by 1 unit rectangle
  2. Sample response: I knew that 4 fives is 20 so I drew a square. I tried going over 10 units but then it was going to take more than 10 units to get back. So, I went over 9 units and up 1 unit and then could do the same again to get back.

Problem 3

Find the perimeter of each shape. Explain or show your reasoning.

  1.  

    Diagram. Rectangle with two sides 11 centimeters and two sides 6 centimeters.

  2.  

    Diagram. Parallelogram with two sides 12 centimeters and two sides 5 centimeters.

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Solution
  1. 34 cm. Sample response: There are 2 sides of length 11 cm so that’s 22 cm and 2 sides of length 6 cm so that’s 12 more making 34.
  2. 34 cm. Sample response: 12+12=2412 + 12 = 24 and 5+5=105 + 5 = 10. 24+10=3424 + 10 = 34.

Problem 4

This hexagon has all equal sides. The perimeter of the hexagon is 96 cm. What are its side lengths? Explain or show your reasoning.

Hexagon.

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Solution

16 cm. Sample response: There are 6 sides so I need to divide 96 by 6.

6×10=606 \times 10 = 60 and 6×6=366 \times 6 = 36, so 6×16=966 \times 16 = 96.

Problem 5

The side length of every pattern block is 1 inch.

A shape with many sides.

  1. What is the perimeter of the entire figure formed by all the blocks? Explain your reasoning.
  2. What is the perimeter of the figure if you remove the skinny rhombuses around the boundary?
  3. What is the perimeter if you next remove the blue rhombuses around the boundary? What if you keep removing more shapes?
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Solution
  1. 24 inches. Sample response: there are 12 skinny rhombuses total and each one has two sides of 1 inch.
  2. 24 inches. Sample response: now there are 12 blue rhombuses around the shape and each one has two sides of 1 inch.
  3. It’s always 24 inches. Sample response: There are always 12 shapes around the edge each with two sides of one inch. (First it’s skinny rhombuses, then blue rhombus, then squares, then blue rhombuses, and then skinny rhombuses again.)

Problem 6

Dot grid.

  1. Draw some different shapes that you can find the perimeter of. Then find their perimeters.
  2. Can you draw a rectangle whose perimeter is an odd number of units? Explain or show your reasoning.
  3. Can you draw a pentagon or hexagon (or a figure with even more sides) whose perimeter is an odd number of units?
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Solution

Sample responses:

  1.  
    Two shapes on dot grid.
    The perimeter of P is 30 units. The perimeter of T is 22 units.
  2. No, there are 2 sides of each length so that means it is an even number.
  3. I tried many shapes and I always got an even number for the perimeter. I can’t do it on this dot paper, but if I could make a pentagon and each side length was 1, then it would add up to 5, which is an odd number.