Grade 6 Math · Topic 53

Area of Parallelograms

A parallelogram is a four-sided shape with two pairs of parallel sides. Cut a triangle off one end and slide it to the other side, and you get a rectangle — which is why a parallelogram's area uses the same formula: base × height. The height is the perpendicular distance between the bases, not the slanted side.

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

Explore visually

Explore a parallelogram

Slide the top edge without changing the base or perpendicular height. Area stays base × height.

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

A parallelogram has base 10 cm and height 6 cm. Find its area.

Use the area formula and substitute the given numbers: A = b × h = 10 × 6 = 60 cm².

Answer: 60 cm²

Worked example 2

Find the area of a parallelogram with b = 12 in and h = 4.5 in.

Use the area formula and substitute the given numbers: A = 12 × 4.5 = 54 in².

Answer: 54 in²

Try a few on your own

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

  1. b = 5, h = 3
    Check

    15

  2. b = 8, h = 6
    Check

    48

  3. b = 10, h = 7
    Check

    70

  4. b = 9, h = 4
    Check

    36

  5. b = 12, h = 5
    Check

    60

  6. b = 15, h = 8
    Check

    120

  7. b = 6.5, h = 4
    Check

    26

  8. b = 20, h = 12
    Check

    240

Try this situation 1

A flag is a parallelogram with base 24 in and height 16 in. How much fabric is needed?

Show a worked solution

Answer: 384 in².

Use the area formula and substitute the given numbers: A = 24 × 16 = 384.

Try this situation 2

A parallelogram-shaped tile has area 84 ft² and base 14 ft. Find its height.

Show a worked solution

Answer: 6 ft.

Use the area formula and substitute the given numbers: A = bh ⇒ 84 = 14h ⇒ h = 6.

Fresh questions · saved on this device

Practice this skill

10 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 parallelogram has base 9 cm and perpendicular height 4 cm. What is its area?

2. A parallelogram has area 126 cm² and perpendicular height 7 cm. What is its base?

3. A parallelogram has base 12 m and area 72 m². What is its perpendicular height?

4. What is the area of a parallelogram with base 15 ft and height 8 ft?

5. A parallelogram is 11 cm along its base and 5 cm tall. Find its area.

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

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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 ↗