Grade 6 Math · Topic 55

Area of Trapezoids

A trapezoid has exactly one pair of parallel sides, called bases (b₁ and b₂). Its area is the average of the bases times the height. The height h is the perpendicular distance between the two bases.

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

Explore visually

Explore a trapezoid

Change both parallel bases and the perpendicular height. The dashed segment shows the 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.

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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

A trapezoid has bases 8 cm and 12 cm, and height 5 cm. Find the area.

Use the area formula and substitute the given numbers: A = 1/2(8 + 12)(5) = 1/2(20)(5) = 50 cm².

Answer: 50 cm²

Worked example 2

A trapezoid has b₁ = 6 in, b₂ = 10 in, and h = 4 in.

Use the area formula and substitute the given numbers: A = 1/2(6 + 10)(4) = 1/2(16)(4) = 32 in².

Answer: 32 in²

Try a few on your own

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

  1. b₁ = 4, b₂ = 6, h = 3
    Check

    15

  2. b₁ = 7, b₂ = 9, h = 4
    Check

    32

  3. b₁ = 5, b₂ = 11, h = 6
    Check

    48

  4. b₁ = 8, b₂ = 14, h = 5
    Check

    55

  5. b₁ = 10, b₂ = 12, h = 8
    Check

    88

  6. b₁ = 3, b₂ = 9, h = 4
    Check

    24

  7. b₁ = 12, b₂ = 18, h = 10
    Check

    150

  8. b₁ = 6, b₂ = 10, h = 7
    Check

    56

Try this situation 1

A trapezoid-shaped patio has bases 9 ft and 15 ft and height 8 ft. Find the area.

Show a worked solution

Answer: 96 ft².

Use the area formula and substitute the given numbers: A = 1/2(9 + 15)(8) = 1/2(24)(8) = 96.

Try this situation 2

A trapezoidal table has area 72 in², height 6 in, and one base of 10 in. Find the other base.

Show a worked solution

Answer: 14 in.

Start by writing the calculation clearly: 72 = 1/2(10 + b₂)(6) ⇒ 72 = 3(10 + b₂) ⇒ 24 = 10 + b₂ ⇒ b₂ = 14.

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 trapezoid has parallel sides of lengths 6 cm and 10 cm, and a height of 4 cm. What is the area?

2. A trapezoid has bases of 18 cm and 12 cm, and a height of 8 cm. What is the area?

3. A garden plot is shaped like a trapezoid with bases of 10 m and 18 m, and a height of 5 m. What is the area?

4. A trapezoid has parallel sides of 8 cm and 12 cm, and a height of 5 cm. What is the area?

5. The bases of a trapezoid are 15 m and 21 m, and the height is h meters. Which equation represents the area A?

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.

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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 ↗