Section B: Practice Problems What is Perimeter?

Section Summary


In this section, we learned that perimeter is the boundary of a flat shape.

We can find the length of a perimeter by adding the lengths of all the sides, or by using multiplication when there are sides with the same length.

rectangle with one side labeled 21 cm and another side labeled 9 cm

We used our knowledge of shapes to find the perimeter even when some side lengths were missing, and to use the perimeter to find missing side lengths.

For example, if we know the perimeter of this rectangle is 32 feet, we can find the lengths of the three unlabeled sides.

rectangle with one side labeled 12 feet

Problem 1 (Lesson 6)

Find the perimeter of each shape.

  1. 8-sided shape on dot grid.
  2. 8-sided shape with perimeter marked with tick marks.

Problem 2 (Lesson 7)

  1. Draw 2 different shapes with perimeter 20 units.

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

Problem 3 (Lesson 8)

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


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

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

Problem 4 (Lesson 9)

All sides of this hexagon have the same length. The perimeter of the hexagon is 96 cm. What are its side lengths? Explain or show your reasoning.


Problem 5 (Exploration)

The side length of every pattern block is 1 inch.

A shape with many sides.
  1. What is the perimeter of the shape? Explain your reasoning.

  2. What is the perimeter of the shape if you remove the skinny rhombuses around the boundary?

  3. What is the perimeter if you next remove the blue rhombuses? What if you keep removing more shapes?

Problem 6 (Exploration)

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 odd? Explain or show your reasoning.

  3. Can you draw a pentagon or hexagon (or a figure with even more sides) whose perimeter is odd?