Learn on PengiSaxon Math, Course 1Chapter 4: Number, Operations, and Measurement

Lesson 31: Areas of Rectangles

In this Grade 6 Saxon Math Course 1 lesson, students learn how to calculate the area of rectangles and squares by multiplying length by width and expressing answers in square units such as square inches, square feet, and square centimeters. The lesson distinguishes area from perimeter and introduces the concept of square units as a measurement of surface. Students also practice working backward from a known area to find the side length and perimeter of a square.

Section 1

📘 Areas of Rectangles

New Concept

The area of a shape is the amount of surface enclosed by its sides. We calculate a rectangle's area by multiplying its length and width.

Length×width=area \text{Length} \times \text{width} = \text{area}

What’s next

This is just the beginning of measuring surfaces. Next, you'll solve problems to find the area of rectangles and squares, and even work backward to find side lengths.

Section 2

Area

Property

The area of a shape is the amount of surface enclosed by its sides. We measure area in square units.

Examples

  • The area of a bedroom floor is best measured in square feet.
  • A playing card's area would be measured in square inches.
  • The total land area of a large city is measured in square miles.

Explanation

Think of area as the amount of paint needed to cover a wall or the number of square tiles to cover a floor. While perimeter measures the distance around a shape, area measures the total space inside it. We use special units like square feet or square meters to count up all that interior space accurately.

Section 3

Area of a Rectangle

Property

To find the area of a rectangle, use the formula:

Length×width=area \text{Length} \times \text{width} = \text{area}

Examples

  • A garden is 10 feet long and 5 feet wide. Its area is 10 ft×5 ft=50 sq. ft10 \text{ ft} \times 5 \text{ ft} = 50 \text{ sq. ft}.
  • A sheet of paper is 11 inches long and 8 inches wide. Its area is 11 in×8 in=88 sq. in11 \text{ in} \times 8 \text{ in} = 88 \text{ sq. in}.
  • A soccer field is 100 meters long and 60 meters wide. Its area is 100 m×60 m=6000 sq. m100 \text{ m} \times 60 \text{ m} = 6000 \text{ sq. m}.

Explanation

Instead of counting every single square unit inside a rectangle one by one, there's a fantastic shortcut! Just multiply the length of the rectangle by its width. This calculation instantly tells you how many square units are needed to fill the entire shape. It's the quickest way to find the total space inside any rectangle.

Section 4

Finding a Square's Side from its Area

Property

If you know the area of a square, you can find its side length by figuring out which number, when multiplied by itself, equals the area.

Examples

  • A square has an area of 49 sq. ft. Since 7×7=497 \times 7 = 49, each side is 7 feet long.
  • A square has an area of 81 sq. cm. Since 9×9=819 \times 9 = 81, each side is 9 centimeters long.
  • A square has an area of 144 sq. in. Since 12×12=14412 \times 12 = 144, each side is 12 inches long.

Explanation

This is like solving a puzzle in reverse! Since a square's length and width are identical, its area is simply side × side. So, if a square has an area of 25 square units, you just ask yourself, 'What number times itself makes 25?' The answer, 5, is the length of each side. It's a neat trick!

Book overview

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

Continue this chapter

Chapter 4: Number, Operations, and Measurement

  1. Lesson 1Current

    Lesson 31: Areas of Rectangles

  2. Lesson 2

    Lesson 32: Expanded Notation

  3. Lesson 3

    Lesson 33: Writing Percents as Fractions, Part 1

  4. Lesson 4

    Lesson 34: Decimal Place Value

  5. Lesson 5

    Lesson 35: Writing Decimal Numbers as Fractions, Part 1

  6. Lesson 6

    Lesson 36: Subtracting Fractions and Mixed Numbers from Whole Numbers

  7. Lesson 7

    Lesson 37: Adding and Subtracting Decimal Numbers

  8. Lesson 8

    Lesson 38: Adding and Subtracting Decimal Numbers and Whole Numbers

  9. Lesson 9

    Lesson 39: Multiplying Decimal Numbers

  10. Lesson 10

    Lesson 40: Using Zero as a Placeholder

  11. Lesson 11

    Investigation 4: Collecting, Organizing, Displaying, and Interpreting Data

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Areas of Rectangles

New Concept

The area of a shape is the amount of surface enclosed by its sides. We calculate a rectangle's area by multiplying its length and width.

Length×width=area \text{Length} \times \text{width} = \text{area}

What’s next

This is just the beginning of measuring surfaces. Next, you'll solve problems to find the area of rectangles and squares, and even work backward to find side lengths.

Section 2

Area

Property

The area of a shape is the amount of surface enclosed by its sides. We measure area in square units.

Examples

  • The area of a bedroom floor is best measured in square feet.
  • A playing card's area would be measured in square inches.
  • The total land area of a large city is measured in square miles.

Explanation

Think of area as the amount of paint needed to cover a wall or the number of square tiles to cover a floor. While perimeter measures the distance around a shape, area measures the total space inside it. We use special units like square feet or square meters to count up all that interior space accurately.

Section 3

Area of a Rectangle

Property

To find the area of a rectangle, use the formula:

Length×width=area \text{Length} \times \text{width} = \text{area}

Examples

  • A garden is 10 feet long and 5 feet wide. Its area is 10 ft×5 ft=50 sq. ft10 \text{ ft} \times 5 \text{ ft} = 50 \text{ sq. ft}.
  • A sheet of paper is 11 inches long and 8 inches wide. Its area is 11 in×8 in=88 sq. in11 \text{ in} \times 8 \text{ in} = 88 \text{ sq. in}.
  • A soccer field is 100 meters long and 60 meters wide. Its area is 100 m×60 m=6000 sq. m100 \text{ m} \times 60 \text{ m} = 6000 \text{ sq. m}.

Explanation

Instead of counting every single square unit inside a rectangle one by one, there's a fantastic shortcut! Just multiply the length of the rectangle by its width. This calculation instantly tells you how many square units are needed to fill the entire shape. It's the quickest way to find the total space inside any rectangle.

Section 4

Finding a Square's Side from its Area

Property

If you know the area of a square, you can find its side length by figuring out which number, when multiplied by itself, equals the area.

Examples

  • A square has an area of 49 sq. ft. Since 7×7=497 \times 7 = 49, each side is 7 feet long.
  • A square has an area of 81 sq. cm. Since 9×9=819 \times 9 = 81, each side is 9 centimeters long.
  • A square has an area of 144 sq. in. Since 12×12=14412 \times 12 = 144, each side is 12 inches long.

Explanation

This is like solving a puzzle in reverse! Since a square's length and width are identical, its area is simply side × side. So, if a square has an area of 25 square units, you just ask yourself, 'What number times itself makes 25?' The answer, 5, is the length of each side. It's a neat trick!

Book overview

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

Continue this chapter

Chapter 4: Number, Operations, and Measurement

  1. Lesson 1Current

    Lesson 31: Areas of Rectangles

  2. Lesson 2

    Lesson 32: Expanded Notation

  3. Lesson 3

    Lesson 33: Writing Percents as Fractions, Part 1

  4. Lesson 4

    Lesson 34: Decimal Place Value

  5. Lesson 5

    Lesson 35: Writing Decimal Numbers as Fractions, Part 1

  6. Lesson 6

    Lesson 36: Subtracting Fractions and Mixed Numbers from Whole Numbers

  7. Lesson 7

    Lesson 37: Adding and Subtracting Decimal Numbers

  8. Lesson 8

    Lesson 38: Adding and Subtracting Decimal Numbers and Whole Numbers

  9. Lesson 9

    Lesson 39: Multiplying Decimal Numbers

  10. Lesson 10

    Lesson 40: Using Zero as a Placeholder

  11. Lesson 11

    Investigation 4: Collecting, Organizing, Displaying, and Interpreting Data