Learn on PengiSaxon Math, Course 1Chapter 1: Number, Operations, and Algebra

Lesson 8: Perimeter

In Lesson 8 of Saxon Math Course 1, Grade 6 students learn how to calculate perimeter by adding the side lengths of polygons, including rectangles, triangles, squares, and trapezoids. The lesson also introduces the concept that for regular polygons, the perimeter can be found by multiplying the length of one side by the number of sides. Students practice finding missing side lengths when the perimeter of a shape is known, such as determining a side of a square from its total perimeter.

Section 1

📘 Perimeter

New Concept

The distance around a shape is its perimeter. To find the perimeter of a polygon, we add the lengths of its sides.

What’s next

This is your introduction to measuring geometric figures. Next, you’ll tackle worked examples to calculate the perimeter of various shapes, including regular polygons, and solve problems from a new perspective.

Section 2

Perimeter of a square

Property

Since a square has four sides of equal length, its perimeter PP is four times the side length ss, so P=4sP = 4s. To find the side length from the perimeter, you can calculate s=P÷4s = P \div 4.

Examples

  • A square with 12-inch sides has a perimeter of 4×12 inches=48 inches4 \times 12 \text{ inches} = 48 \text{ inches}.
  • If a square's perimeter is 20 cm, the length of each side is 20 cm÷4=5 cm20 \text{ cm} \div 4 = 5 \text{ cm}.
  • A square field with a perimeter of 400 meters has sides that are each 400 m÷4=100 m400 \text{ m} \div 4 = 100 \text{ m} long.

Explanation

A square is a super special shape where all sides are best friends and insist on being the exact same length! So, instead of adding the same number four times, you can just use a quick multiplication shortcut. Finding the length of a side from the perimeter is just doing that same cool trick in reverse. Teamwork for numbers!

Section 3

Perimeter of a regular polygon

Property

A regular polygon has sides that are all the same length. To find its perimeter, multiply the number of sides by the length of one side.

Examples

  • An equilateral triangle (3 sides) with 2 cm sides has a perimeter of 3×2 cm=6 cm3 \times 2 \text{ cm} = 6 \text{ cm}.
  • A regular pentagon (5 sides) with 10 mm sides has a perimeter of 5×10 mm=50 mm5 \times 10 \text{ mm} = 50 \text{ mm}.
  • A regular octagon (8 sides) where each side is 5 inches long has a perimeter of 8×5 inches=40 inches8 \times 5 \text{ inches} = 40 \text{ inches}.

Explanation

Regular polygons are all about fairness! Every single side is the exact same length. This makes finding the perimeter a total breeze. Instead of adding a long list of the same number over and over again, you can just multiply the number of sides by the length of one side. It is the ultimate mathematical shortcut for these shapes!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Number, Operations, and Algebra

  1. Lesson 1

    Lesson 1: Adding Whole Numbers and Money

  2. Lesson 2

    Lesson 2: Multiplying Whole Numbers and Money

  3. Lesson 3

    Lesson 3: Unknown Numbers in Addition

  4. Lesson 4

    Lesson 4: Unknown Numbers in Multiplication

  5. Lesson 5

    Lesson 5: Order of Operations, Part 1

  6. Lesson 6

    Lesson 6: Fractional Parts

  7. Lesson 7

    Lesson 7: Lines, Segments, and Rays

  8. Lesson 8Current

    Lesson 8: Perimeter

  9. Lesson 9

    Lesson 9: The Number Line: Ordering and Comparing

  10. Lesson 10

    Lesson 10: Sequences

  11. Lesson 11

    Investigation 1: Frequency Tables, Histograms, Surveys

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Perimeter

New Concept

The distance around a shape is its perimeter. To find the perimeter of a polygon, we add the lengths of its sides.

What’s next

This is your introduction to measuring geometric figures. Next, you’ll tackle worked examples to calculate the perimeter of various shapes, including regular polygons, and solve problems from a new perspective.

Section 2

Perimeter of a square

Property

Since a square has four sides of equal length, its perimeter PP is four times the side length ss, so P=4sP = 4s. To find the side length from the perimeter, you can calculate s=P÷4s = P \div 4.

Examples

  • A square with 12-inch sides has a perimeter of 4×12 inches=48 inches4 \times 12 \text{ inches} = 48 \text{ inches}.
  • If a square's perimeter is 20 cm, the length of each side is 20 cm÷4=5 cm20 \text{ cm} \div 4 = 5 \text{ cm}.
  • A square field with a perimeter of 400 meters has sides that are each 400 m÷4=100 m400 \text{ m} \div 4 = 100 \text{ m} long.

Explanation

A square is a super special shape where all sides are best friends and insist on being the exact same length! So, instead of adding the same number four times, you can just use a quick multiplication shortcut. Finding the length of a side from the perimeter is just doing that same cool trick in reverse. Teamwork for numbers!

Section 3

Perimeter of a regular polygon

Property

A regular polygon has sides that are all the same length. To find its perimeter, multiply the number of sides by the length of one side.

Examples

  • An equilateral triangle (3 sides) with 2 cm sides has a perimeter of 3×2 cm=6 cm3 \times 2 \text{ cm} = 6 \text{ cm}.
  • A regular pentagon (5 sides) with 10 mm sides has a perimeter of 5×10 mm=50 mm5 \times 10 \text{ mm} = 50 \text{ mm}.
  • A regular octagon (8 sides) where each side is 5 inches long has a perimeter of 8×5 inches=40 inches8 \times 5 \text{ inches} = 40 \text{ inches}.

Explanation

Regular polygons are all about fairness! Every single side is the exact same length. This makes finding the perimeter a total breeze. Instead of adding a long list of the same number over and over again, you can just multiply the number of sides by the length of one side. It is the ultimate mathematical shortcut for these shapes!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Number, Operations, and Algebra

  1. Lesson 1

    Lesson 1: Adding Whole Numbers and Money

  2. Lesson 2

    Lesson 2: Multiplying Whole Numbers and Money

  3. Lesson 3

    Lesson 3: Unknown Numbers in Addition

  4. Lesson 4

    Lesson 4: Unknown Numbers in Multiplication

  5. Lesson 5

    Lesson 5: Order of Operations, Part 1

  6. Lesson 6

    Lesson 6: Fractional Parts

  7. Lesson 7

    Lesson 7: Lines, Segments, and Rays

  8. Lesson 8Current

    Lesson 8: Perimeter

  9. Lesson 9

    Lesson 9: The Number Line: Ordering and Comparing

  10. Lesson 10

    Lesson 10: Sequences

  11. Lesson 11

    Investigation 1: Frequency Tables, Histograms, Surveys