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Chapter 44: Perimeter and Circumference

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

44.1 Perimeter

Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Perimeter.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the perimeter of a rectangle 5 cm by 2 cm.

  1. Use P = 2(l+w).
  2. P = 2(5+2).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 14 cm

Worked Example 2

Problem: Find the perimeter of a rectangle 6 cm by 3 cm.

  1. Use P = 2(l+w).
  2. P = 2(6+3).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 18 cm

Worked Example 3

Problem: Find the perimeter of a rectangle 7 cm by 4 cm.

  1. Use P = 2(l+w).
  2. P = 2(7+4).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 22 cm

Worked Example 4

Problem: Find the perimeter of a rectangle 8 cm by 5 cm.

  1. Use P = 2(l+w).
  2. P = 2(8+5).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 26 cm

Worked Example 5

Problem: Find the perimeter of a rectangle 9 cm by 6 cm.

  1. Use P = 2(l+w).
  2. P = 2(9+6).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 30 cm

Worked Example 6

Problem: Find the perimeter of a rectangle 10 cm by 7 cm.

  1. Use P = 2(l+w).
  2. P = 2(10+7).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 34 cm

Worked Example 7

Problem: Find the perimeter of a rectangle 11 cm by 8 cm.

  1. Use P = 2(l+w).
  2. P = 2(11+8).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 38 cm

Worked Example 8

Problem: Find the perimeter of a rectangle 12 cm by 9 cm.

  1. Use P = 2(l+w).
  2. P = 2(12+9).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 42 cm

Worked Example 9

Problem: Find the perimeter of a rectangle 13 cm by 10 cm.

  1. Use P = 2(l+w).
  2. P = 2(13+10).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 46 cm

Worked Example 10

Problem: Find the perimeter of a rectangle 14 cm by 11 cm.

  1. Use P = 2(l+w).
  2. P = 2(14+11).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 50 cm

Practice exercise

Create one new Grade 8 problem involving Perimeter. Show the important steps, include units when needed, and explain how you checked the answer.

44.2 Rectangle perimeter

An angle is formed by two rays meeting at a vertex and is measured in degrees. In this section, the focus is Rectangle perimeter.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the supplementary angle to 35°.

  1. Supplementary angles total 180°.
  2. 180° - 35° = 145°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 145°

Worked Example 2

Problem: Find the supplementary angle to 48°.

  1. Supplementary angles total 180°.
  2. 180° - 48° = 132°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 132°

Worked Example 3

Problem: Find the supplementary angle to 67°.

  1. Supplementary angles total 180°.
  2. 180° - 67° = 113°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 113°

Worked Example 4

Problem: Find the supplementary angle to 72°.

  1. Supplementary angles total 180°.
  2. 180° - 72° = 108°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 108°

Worked Example 5

Problem: Find the supplementary angle to 110°.

  1. Supplementary angles total 180°.
  2. 180° - 110° = 70°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 70°

Worked Example 6

Problem: Find the supplementary angle to 25°.

  1. Supplementary angles total 180°.
  2. 180° - 25° = 155°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 155°

Worked Example 7

Problem: Find the supplementary angle to 58°.

  1. Supplementary angles total 180°.
  2. 180° - 58° = 122°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 122°

Worked Example 8

Problem: Find the supplementary angle to 83°.

  1. Supplementary angles total 180°.
  2. 180° - 83° = 97°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 97°

Worked Example 9

Problem: Find the supplementary angle to 95°.

  1. Supplementary angles total 180°.
  2. 180° - 95° = 85°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 85°

Worked Example 10

Problem: Find the supplementary angle to 120°.

  1. Supplementary angles total 180°.
  2. 180° - 120° = 60°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 60°

Practice exercise

Create one new Grade 8 problem involving Rectangle perimeter. Show the important steps, include units when needed, and explain how you checked the answer.

44.3 Square perimeter

Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Square perimeter.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the supplementary angle to 35°.

  1. Supplementary angles total 180°.
  2. 180° - 35° = 145°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 145°

Worked Example 2

Problem: Find the supplementary angle to 48°.

  1. Supplementary angles total 180°.
  2. 180° - 48° = 132°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 132°

Worked Example 3

Problem: Find the supplementary angle to 67°.

  1. Supplementary angles total 180°.
  2. 180° - 67° = 113°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 113°

Worked Example 4

Problem: Find the supplementary angle to 72°.

  1. Supplementary angles total 180°.
  2. 180° - 72° = 108°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 108°

Worked Example 5

Problem: Find the supplementary angle to 110°.

  1. Supplementary angles total 180°.
  2. 180° - 110° = 70°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 70°

Worked Example 6

Problem: Find the supplementary angle to 25°.

  1. Supplementary angles total 180°.
  2. 180° - 25° = 155°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 155°

Worked Example 7

Problem: Find the supplementary angle to 58°.

  1. Supplementary angles total 180°.
  2. 180° - 58° = 122°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 122°

Worked Example 8

Problem: Find the supplementary angle to 83°.

  1. Supplementary angles total 180°.
  2. 180° - 83° = 97°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 97°

Worked Example 9

Problem: Find the supplementary angle to 95°.

  1. Supplementary angles total 180°.
  2. 180° - 95° = 85°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 85°

Worked Example 10

Problem: Find the supplementary angle to 120°.

  1. Supplementary angles total 180°.
  2. 180° - 120° = 60°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 60°

Practice exercise

Create one new Grade 8 problem involving Square perimeter. Show the important steps, include units when needed, and explain how you checked the answer.

44.4 Triangle perimeter

An angle is formed by two rays meeting at a vertex and is measured in degrees. In this section, the focus is Triangle perimeter.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A triangle has angles 35° and 45°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-35-45=100.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 100°

Worked Example 2

Problem: A triangle has angles 48° and 58°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-48-58=74.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 74°

Worked Example 3

Problem: A triangle has angles 67° and 47°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-67-47=66.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 66°

Worked Example 4

Problem: A triangle has angles 72° and 52°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-72-52=56.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 56°

Worked Example 5

Problem: A triangle has angles 110° and 60°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-110-60=10.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 10°

Worked Example 6

Problem: A triangle has angles 25° and 65°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-25-65=90.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 90°

Worked Example 7

Problem: A triangle has angles 58° and 68°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-58-68=54.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 54°

Worked Example 8

Problem: A triangle has angles 83° and 63°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-83-63=34.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 34°

Worked Example 9

Problem: A triangle has angles 95° and 45°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-95-45=40.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 40°

Worked Example 10

Problem: A triangle has angles 120° and 40°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-120-40=20.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 20°

Practice exercise

Create one new Grade 8 problem involving Triangle perimeter. Show the important steps, include units when needed, and explain how you checked the answer.

44.5 Irregular figures

Irregular figures is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Irregular figures: Explain Irregular figures in one simple sentence.

  1. Look at the words in “Irregular figures”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: Irregular figures is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Irregular figures: A student says, “I can use Irregular figures without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: Irregular figures: What is the first step when solving a problem about Irregular figures?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: Irregular figures: After solving a Irregular figures problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: Irregular figures: Give one way Irregular figures could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: Irregular figures can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Irregular figures: Which representation could help explain Irregular figures: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: Irregular figures: A student gets an answer for Irregular figures but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: Irregular figures: Why can estimation help before a detailed Irregular figures calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: Irregular figures: How can you test whether your rule for Irregular figures works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: Irregular figures: How would you teach Irregular figures to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving Irregular figures. Show the important steps, include units when needed, and explain how you checked the answer.

44.6 Circle radius

Circle radius is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A circle has radius 2 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(2).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 12.57 cm

Worked Example 2

Problem: A circle has radius 3 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(3).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 18.85 cm

Worked Example 3

Problem: A circle has radius 4 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(4).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 25.13 cm

Worked Example 4

Problem: A circle has radius 5 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(5).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 31.42 cm

Worked Example 5

Problem: A circle has radius 6 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(6).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 37.70 cm

Worked Example 6

Problem: A circle has radius 7 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(7).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 43.98 cm

Worked Example 7

Problem: A circle has radius 8 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(8).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 50.27 cm

Worked Example 8

Problem: A circle has radius 9 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(9).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 56.55 cm

Worked Example 9

Problem: A circle has radius 10 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(10).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 62.83 cm

Worked Example 10

Problem: A circle has radius 11 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(11).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 69.12 cm

Practice exercise

Create one new Grade 8 problem involving Circle radius. Show the important steps, include units when needed, and explain how you checked the answer.

44.7 Circle diameter

Circle diameter is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A circle has radius 2 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(2).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 12.57 cm

Worked Example 2

Problem: A circle has radius 3 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(3).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 18.85 cm

Worked Example 3

Problem: A circle has radius 4 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(4).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 25.13 cm

Worked Example 4

Problem: A circle has radius 5 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(5).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 31.42 cm

Worked Example 5

Problem: A circle has radius 6 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(6).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 37.70 cm

Worked Example 6

Problem: A circle has radius 7 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(7).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 43.98 cm

Worked Example 7

Problem: A circle has radius 8 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(8).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 50.27 cm

Worked Example 8

Problem: A circle has radius 9 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(9).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 56.55 cm

Worked Example 9

Problem: A circle has radius 10 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(10).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 62.83 cm

Worked Example 10

Problem: A circle has radius 11 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(11).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 69.12 cm

Practice exercise

Create one new Grade 8 problem involving Circle diameter. Show the important steps, include units when needed, and explain how you checked the answer.

44.8 Pi

Pi is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A circle has radius 2 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(2).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 12.57 cm

Worked Example 2

Problem: A circle has radius 3 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(3).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 18.85 cm

Worked Example 3

Problem: A circle has radius 4 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(4).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 25.13 cm

Worked Example 4

Problem: A circle has radius 5 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(5).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 31.42 cm

Worked Example 5

Problem: A circle has radius 6 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(6).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 37.70 cm

Worked Example 6

Problem: A circle has radius 7 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(7).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 43.98 cm

Worked Example 7

Problem: A circle has radius 8 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(8).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 50.27 cm

Worked Example 8

Problem: A circle has radius 9 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(9).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 56.55 cm

Worked Example 9

Problem: A circle has radius 10 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(10).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 62.83 cm

Worked Example 10

Problem: A circle has radius 11 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(11).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 69.12 cm

Practice exercise

Create one new Grade 8 problem involving Pi. Show the important steps, include units when needed, and explain how you checked the answer.

44.9 Circumference

Circumference is the distance around a circle. In this section, the focus is Circumference.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A circle has radius 2 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(2).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 12.57 cm

Worked Example 2

Problem: A circle has radius 3 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(3).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 18.85 cm

Worked Example 3

Problem: A circle has radius 4 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(4).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 25.13 cm

Worked Example 4

Problem: A circle has radius 5 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(5).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 31.42 cm

Worked Example 5

Problem: A circle has radius 6 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(6).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 37.70 cm

Worked Example 6

Problem: A circle has radius 7 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(7).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 43.98 cm

Worked Example 7

Problem: A circle has radius 8 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(8).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 50.27 cm

Worked Example 8

Problem: A circle has radius 9 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(9).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 56.55 cm

Worked Example 9

Problem: A circle has radius 10 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(10).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 62.83 cm

Worked Example 10

Problem: A circle has radius 11 cm. Find its circumference.

  1. Use C = 2πr.
  2. C = 2π(11).
  3. Use π ≈ 3.1416 if a decimal is needed.

Very beginner explanation: Circumference is the distance around a circle. Radius is half the diameter.

Answer: 69.12 cm

Practice exercise

Create one new Grade 8 problem involving Circumference. Show the important steps, include units when needed, and explain how you checked the answer.

44.10 C = πd

C = πd is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: C = πd: Explain C = πd in one simple sentence.

  1. Look at the words in “C = πd”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: C = πd is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: C = πd: A student says, “I can use C = πd without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: C = πd: What is the first step when solving a problem about C = πd?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: C = πd: After solving a C = πd problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: C = πd: Give one way C = πd could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: C = πd can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: C = πd: Which representation could help explain C = πd: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: C = πd: A student gets an answer for C = πd but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: C = πd: Why can estimation help before a detailed C = πd calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: C = πd: How can you test whether your rule for C = πd works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: C = πd: How would you teach C = πd to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving C = πd. Show the important steps, include units when needed, and explain how you checked the answer.

44.11 C = 2πr

C = 2πr is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: C = 2πr: Explain C = 2πr in one simple sentence.

  1. Look at the words in “C = 2πr”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: C = 2πr is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: C = 2πr: A student says, “I can use C = 2πr without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: C = 2πr: What is the first step when solving a problem about C = 2πr?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: C = 2πr: After solving a C = 2πr problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: C = 2πr: Give one way C = 2πr could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: C = 2πr can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: C = 2πr: Which representation could help explain C = 2πr: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: C = 2πr: A student gets an answer for C = 2πr but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: C = 2πr: Why can estimation help before a detailed C = 2πr calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: C = 2πr: How can you test whether your rule for C = 2πr works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: C = 2πr: How would you teach C = 2πr to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving C = 2πr. Show the important steps, include units when needed, and explain how you checked the answer.

44.12 Composite perimeter problems

Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Composite perimeter problems.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the area of a rectangle 6 cm by 3 cm.

  1. Use A = length × width.
  2. A = 6×3.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 18 cm²

Worked Example 2

Problem: Find the area of a rectangle 7 cm by 4 cm.

  1. Use A = length × width.
  2. A = 7×4.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 28 cm²

Worked Example 3

Problem: Find the area of a rectangle 8 cm by 5 cm.

  1. Use A = length × width.
  2. A = 8×5.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 40 cm²

Worked Example 4

Problem: Find the area of a rectangle 9 cm by 6 cm.

  1. Use A = length × width.
  2. A = 9×6.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 54 cm²

Worked Example 5

Problem: Find the area of a rectangle 10 cm by 7 cm.

  1. Use A = length × width.
  2. A = 10×7.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 70 cm²

Worked Example 6

Problem: Find the area of a rectangle 11 cm by 8 cm.

  1. Use A = length × width.
  2. A = 11×8.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 88 cm²

Worked Example 7

Problem: Find the area of a rectangle 12 cm by 9 cm.

  1. Use A = length × width.
  2. A = 12×9.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 108 cm²

Worked Example 8

Problem: Find the area of a rectangle 13 cm by 10 cm.

  1. Use A = length × width.
  2. A = 13×10.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 130 cm²

Worked Example 9

Problem: Find the area of a rectangle 14 cm by 11 cm.

  1. Use A = length × width.
  2. A = 14×11.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 154 cm²

Worked Example 10

Problem: Find the area of a rectangle 15 cm by 12 cm.

  1. Use A = length × width.
  2. A = 15×12.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 180 cm²

Practice exercise

Create one new Grade 8 problem involving Composite perimeter problems. Show the important steps, include units when needed, and explain how you checked the answer.

44.13 Real-life perimeter problems

Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Real-life perimeter problems.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the perimeter of a rectangle 5 cm by 2 cm.

  1. Use P = 2(l+w).
  2. P = 2(5+2).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 14 cm

Worked Example 2

Problem: Find the perimeter of a rectangle 6 cm by 3 cm.

  1. Use P = 2(l+w).
  2. P = 2(6+3).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 18 cm

Worked Example 3

Problem: Find the perimeter of a rectangle 7 cm by 4 cm.

  1. Use P = 2(l+w).
  2. P = 2(7+4).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 22 cm

Worked Example 4

Problem: Find the perimeter of a rectangle 8 cm by 5 cm.

  1. Use P = 2(l+w).
  2. P = 2(8+5).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 26 cm

Worked Example 5

Problem: Find the perimeter of a rectangle 9 cm by 6 cm.

  1. Use P = 2(l+w).
  2. P = 2(9+6).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 30 cm

Worked Example 6

Problem: Find the perimeter of a rectangle 10 cm by 7 cm.

  1. Use P = 2(l+w).
  2. P = 2(10+7).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 34 cm

Worked Example 7

Problem: Find the perimeter of a rectangle 11 cm by 8 cm.

  1. Use P = 2(l+w).
  2. P = 2(11+8).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 38 cm

Worked Example 8

Problem: Find the perimeter of a rectangle 12 cm by 9 cm.

  1. Use P = 2(l+w).
  2. P = 2(12+9).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 42 cm

Worked Example 9

Problem: Find the perimeter of a rectangle 13 cm by 10 cm.

  1. Use P = 2(l+w).
  2. P = 2(13+10).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 46 cm

Worked Example 10

Problem: Find the perimeter of a rectangle 14 cm by 11 cm.

  1. Use P = 2(l+w).
  2. P = 2(14+11).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 50 cm

Practice exercise

Create one new Grade 8 problem involving Real-life perimeter problems. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 44 Review Questions and Answers

Q1. What is important to remember about Perimeter?

Answer: Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Perimeter.

Q2. What is important to remember about Rectangle perimeter?

Answer: An angle is formed by two rays meeting at a vertex and is measured in degrees. In this section, the focus is Rectangle perimeter.

Q3. What is important to remember about Square perimeter?

Answer: Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Square perimeter.

Q4. What is important to remember about Triangle perimeter?

Answer: An angle is formed by two rays meeting at a vertex and is measured in degrees. In this section, the focus is Triangle perimeter.

Q5. What is important to remember about Irregular figures?

Answer: Irregular figures is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q6. What is important to remember about Circle radius?

Answer: Circle radius is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Circle diameter?

Answer: Circle diameter is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Pi?

Answer: Pi is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Circumference?

Answer: Circumference is the distance around a circle. In this section, the focus is Circumference.

Q10. What is important to remember about C = πd?

Answer: C = πd is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q11. What is important to remember about C = 2πr?

Answer: C = 2πr is an important Grade 8 concept in Perimeter and Circumference. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Composite perimeter problems?

Answer: Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Composite perimeter problems.

Q13. What is important to remember about Real-life perimeter problems?

Answer: Perimeter is the total distance around a two-dimensional figure. In this section, the focus is Real-life perimeter problems.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.