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

Lesson 5.35.3 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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. top base and bottom base
ParallelSpanish: Paralelas Two lines or sides that stay the same distance apart and never meet. the two bases
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, meets bases squarely
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 examplefinding a trapezoid's area by decomposing

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

An isosceles trapezoid has a top base of 8 m, a bottom base of 14 m, and a height of 6 m. Find the area.

  1. Decompose it: a rectangle in the middle and two matching triangles on the ends.
  2. Rectangle: top base by height. 8 × 6 = 48
  3. Leftover bottom: 14 − 8 = 6, split evenly into two triangle bases of 3 m.
  4. Each triangle ½ × 3 × 6 = 9, so two give 18. 48 + 18 = 66

Answer: The area of the trapezoid is 66 square meters (66 m²).

Now you trySame steps, your turn

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

An isosceles trapezoid has bases of 12 in. and 20 in. with a height of 7 in. Find the area.

  1. Decompose into a rectangle and two matching triangles. Sketch the cuts.
  2. Rectangle: × = in²
  3. Leftover bottom: − = , so each triangle base is in.
  4. Triangles: + = . Total: + = in²
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 two parallel bases are and .
  • I decomposed the trapezoid into and .
  • The pieces have areas , , and .
  • The total area is square units because .

Word bank trapezoidparallelbaseheightdecomposerectangletriangleleftoveraddtotalareasquare units

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 5.35.3 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Part 1Understand the ideamodels and meaning
  1. 1Complete each step, then write the final answer.

    A parking lot is a trapezoid. Its parallel sides are 90 ft and 60 ft. They are 40 ft apart. Paving costs $3 per square foot. What does it cost to pave the lot?

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    56 m²7 m5 m? m

    A trapezoid has an area of 56 square meters. Its height is 7 m. One base is 5 m. How long is the other base?

    1. 1Double the area to undo the half.
    2. 2Divide by the height. What is the sum of the bases?
    3. 3Subtract the base you know. What is the other base?
    Final answer:
  2. 3Complete each step, then write the final answer.
    45 ft²h = ?6 ft4 ft

    A trapezoid has an area of 45 square feet. Its bases are 4 ft and 6 ft. What is its height?

    1. 1Find the average of the two bases.
    2. 2The area is 5 × h. What is the height?
    3. 3Why can the average base work like a rectangle’s length?
    Final answer:
  3. 4Complete 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:
  4. 5Complete each step, then write the final answer.

    A trapezoid has an area of 66 square inches. Its height is 6 inches. One base is 8 inches. How long is the other base?

    Show your work
    Final answer:
  5. 6Circle 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

Explain your thinkingJay took half of the bases first. The formula takes half at the end. Why do both orders give the same area?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help