Grade 6 Math · Topic 54

Area of Triangles

A triangle is exactly half of a parallelogram with the same base and height. So its area formula is just half of the parallelogram's: A = 1/2 b h. As before, h is the perpendicular height from the base to the opposite vertex.

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

Explore visually

Explore a triangle

Change the base and perpendicular height. Compare its area with a rectangle using the same dimensions.

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.

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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 triangle with b = 10 cm and h = 6 cm.

Use the area formula and substitute the given numbers: A = 1/2(10)(6) = 1/2(60) = 30 cm².

Answer: 30 cm²

Worked example 2

A right triangle has legs 7 in and 9 in. Find its area.

Use the area formula and substitute the given numbers: A = 1/2(7)(9) = 63/2 = 31.5 in².

Answer: 31.5 in²

Try a few on your own

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

  1. b = 6, h = 4
    Check

    12

  2. b = 10, h = 8
    Check

    40

  3. b = 12, h = 5
    Check

    30

  4. b = 9, h = 6
    Check

    27

  5. b = 14, h = 10
    Check

    70

  6. b = 7, h = 4
    Check

    14

  7. b = 15, h = 12
    Check

    90

  8. b = 8.5, h = 6
    Check

    25.5

Try this situation 1

A triangular sail has base 5 ft and height 8 ft. Find its area.

Show a worked solution

Answer: 20 ft².

Use the area formula and substitute the given numbers: A = 1/2(5)(8) = 20.

Try this situation 2

A triangle has area 48 in² and base 12 in. Find its height.

Show a worked solution

Answer: 8 in.

Start by writing the calculation clearly: 1/2(12)h = 48 ⇒ 6h = 48 ⇒ h = 8.

Fresh questions · saved on this device

Practice this skill

11 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 triangular flag has a base of 10 meters and a height of 8 meters. What is the area of the flag?

2. A triangular sail has a base of 12 ft and a height of 9 ft. What is the area?

3. A triangle has base 15 cm and perpendicular height 8 cm. What is its area?

4. A triangular flower bed has a base of 12 meters and a height of 7 meters. What is the area of the flower bed?

5. A triangle has base 14 cm and perpendicular height 6 cm. What is 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 ↗