Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3The Trapezoid Area Formula

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
TrapezoidSpanish: Trapecio A four-sided shape with just one pair of parallel sides. A = ½(b1 + b2)h
ParallelSpanish: Paralelas Two lines or sides that stay the same distance apart and never meet. The top and bottom of a parallelogram never get closer together — matching arrowheads (›) mark one parallel pair, double arrowheads (››) mark the other.
Base 1 (b1)Spanish: Base 1 (b1) One of the two parallel sides of a trapezoid. If the bottom of the trapezoid is 10 ft, then b₁ = 10 ft in the formula A = ½(b₁ + b₂) × h
Base 2 (b2)Spanish: Base 2 (b2) The other parallel side of a trapezoid. If the top of the trapezoid is 6 ft, then b₂ = 6 ft; both bases are parallel to each other
HeightSpanish: Altura The straight-up distance between the two parallel sides. h, at a square corner
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). The dashed height meets the base at a square corner — the small 90° box is what makes it perpendicular, not slanted.

How it worksWorked exampleusing the trapezoid area formula

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A trapezoid has parallel bases of 9 cm and 15 cm and a height of 8 cm. Find the area.

  1. Name the parts. b1 = 9 cm b2 = 15 cm h = 8 cm
  2. Write the formula. A = ½ × (b1 + b2) × h
  3. Add the two bases first. 9 + 15 = 24
  4. Multiply, then halve. 24 × 8 = 192, and half of 192 is 96

Answer: The area of the trapezoid is 96 square centimeters (96 cm²).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A trapezoid has parallel bases of 13 in. and 19 in. and a height of 6 in. Find the area.

  1. Name the parts. b1 = in. b2 = in. h = in.
  2. Write the formula. A = ½ × ( + ) ×
  3. Add the two bases first. + =
  4. Multiply, then halve. × = , half is
Answer:area of the trapezoid

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The parallel bases are and , and the height is .
  • I added the bases first because .
  • A = ½ × ( + ) × = .
  • The answer is in square units because .

Word bank trapezoidbaseheightparallelsumaddhalfformulaareasquare unitsrectangleaverage

Watch outA common mistake

A common mistake in Area of Trapezoids is forgetting the ½ in A = ½ × (b1 + b2) × h. After adding the bases and multiplying by the height, students stop there instead of taking half — for example, with bases 6 ft and 10 ft and a height of 4 ft, they compute (6 + 10) × 4 = 64 sq ft instead of taking half to get the correct 32 sq ft. That unhalved number is really the area of the parallelogram made from two trapezoids, not the area of one trapezoid. Before you submit, always ask: "Did I take half of my last answer?"

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3The Trapezoid Area Formula

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

  1. 1Complete each step, then write the final answer.
    4 m5 m1 m

    A trapezoid has bases of 1 m and 5 m. Its height is 4 m. Find its area.

    Show your work

    Hint Add the bases. Multiply by the height. Then take half.

    Final answer:
  2. 2Complete each step, then write the final answer.

    A trapezoid has bases of 3 ft and 9 ft. Its height is 2 ft. Find its area.

    Show your work

    Hint Add 3 + 9 first.

    Final answer:
  3. 3Complete each step, then write the final answer.

    A garden is a trapezoid. Its parallel sides are 6 m and 8 m. Its height is 5 m. What is its area?

    Show your work

    Hint Add the bases. Multiply by the height. Then take half.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3The Trapezoid Area Formula

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

  1. 1Complete each step, then write the final answer.

    Rosa finds the area of a trapezoid with bases 7 cm and 3 cm and height 6 cm. She writes 7 × 6 = 42. What is the correct area?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    A trapezoid has bases of 2.5 m and 5.5 m. Its height is 6 m. Find its area.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A trapezoid has bases of 4 m and 10 m. Its height is 6 m. Find its area.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3The Trapezoid Area Formula

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

  1. 1Circle the letter of the best answer. Show how you know.

    A trapezoidal window has parallel edges of 4 feet and 8 feet and a height of 5 feet. What is its area?

    1. A17 square feet
    2. B20 square feet
    3. C30 square feet
    4. D60 square feet
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2Circle the letter of the best answer. Show how you know.

    A trapezoid has bases of 6 cm and 14 cm and a height of 5 cm. Jay finds 20 ÷ 2 = 10, then 10 × 5 = 50. Lin finds 6 × 5 + 14 × 5 = 100. Who is right?

    1. AJay: the area is 50 square centimeters
    2. BLin: the area is 100 square centimeters
    3. CBoth are right
    220
  3. 3Complete each step, then write the final answer.

    A trapezoid has an area of 70 square centimeters. Its bases are 6 cm and 8 cm. What is its height?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help