Grade 6 Math · Topic 52

Area of Rectangles and Squares

Area is the amount of space inside a flat shape, measured in square units. For a rectangle, area = length × width. A square is a special rectangle whose sides are all equal, so area = side × side = s².

Lesson alignment: 6.G.A.1 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Change a shape and its dimensions

Compare rectangles, parallelograms, triangles, and trapezoids. The perpendicular height is shown with a dashed line.

Think first: Which measurements determine the area, and which length is the perpendicular height?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the area of a rectangle with ℓ = 8 ft and w = 5 ft.

Use the area formula and substitute the given numbers: A = ℓ w = 8 × 5 = 40 ft².

Answer: 40 ft²

Worked example 2

A square has side 7 cm. Find its area.

Use the area formula and substitute the given numbers: A = s² = 7² = 49 cm².

Answer: 49 cm²

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. Rectangle: ℓ = 6, w = 4
    Check

    24

  2. Rectangle: ℓ = 9, w = 3
    Check

    27

  3. Rectangle: ℓ = 12, w = 5
    Check

    60

  4. Square: s = 4
    Check

    16

  5. Square: s = 8
    Check

    64

  6. Square: s = 11
    Check

    121

  7. Rectangle: ℓ = 7.5, w = 4
    Check

    30

  8. Square: s = 2.5
    Check

    6.25

Try this situation 1

A rectangular garden is 15 ft long and 8 ft wide. How many square feet of soil are needed?

Show a worked solution

Answer: 120 ft².

Use the area formula and substitute the given numbers: A = 15 × 8 = 120.

Try this situation 2

A square poster has area 144 in². How long is each side?

Show a worked solution

Answer: 12 inches.

Start by writing the calculation clearly: s² = 144 ⇒ s = 12.

Fresh questions · saved on this device

Practice this skill

42 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A rectangular room has an area of 120 square meters. If the width is 10 meters, what is the length?

2. A rectangular field is 15 meters long and 8 meters wide. A square plot with side 6 meters is removed from one corner. What is the area of the remaining field?

3. A rectangular poster has a length of 18 inches and a width of 12 inches. What is the area of the poster?

4. A rectangular banner has a length of 20 inches and a width of 14 inches. What is the area of the banner?

5. A square has a side length of 9 inches. What is the area of the square?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Geometry: Area, Surface Area & Volume quiz ↗Try a full practice test ↗