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

Lesson 5.35.1–5.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 5.1–5.3 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Area of ParallelogramsSpanish: Área de paralelogramos The space inside a parallelogram. Formula: A = b × h, using the perpendicular height. A = b × h; if b = 10 cm and h = 6 cm, A = 60 cm².
Slanted sideSpanish: Lado inclinado A side that leans instead of going straight up and down. It is not the perpendicular height. In a leaning parallelogram, use the dashed 90° height—not the slanted side—in A = b × h.
ParallelogramSpanish: Paralelogramo A four-sided shape with two pairs of parallel sides. Think of a leaning door — the top and bottom are parallel, and the two sides are parallel, like a slanted rectangle
ParallelSpanish: Paralelas Two lines or sides that stay the same distance apart and never meet. the two bases
BaseSpanish: Base Any side of a parallelogram can be the base. Once you pick a base, the height must be measured perpendicular (at a 90° angle) to it. b1 (top), b2 (bottom)
HeightSpanish: Altura The straight-up distance from the base to the top. h, meets bases squarely

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 5.35.1–5.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 5.1–5.3 by using each lesson's big idea in mixed practice.

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

    (Lesson 5.1) What is the area of a parallelogram with base 10 cm and height 7 cm?

    1. A17 sq cm
    2. B34 sq cm
    3. C70 sq cm
    4. D70 cm

    Hint You know both the base (10 cm) and the height (7 cm) — this is a direct use of the parallelogram area formula.

    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 5.1) A parallelogram has an area of 54 sq ft and a base of 9 ft. What is the height?

    1. A6 ft
    2. B27 ft
    3. C45 ft
    4. D63 ft

    Hint This time you're given the area (54 sq ft) and the base (9 ft) — the height is the missing piece.

    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 5.2) What is the area of a triangle with base 10 cm and height 6 cm?

    1. A16 sq cm
    2. B30 sq cm
    3. C30 cm
    4. D60 sq cm

    Hint You have a base of 10 cm and a height of 6 cm — a triangle needs only those two, plus one special step.

    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 5.2) A triangle has an area of 24 sq ft and a base of 8 ft. What is the height?

    1. A3 ft
    2. B6 ft
    3. C12 ft
    4. D16 ft

    Hint The area (24 sq ft) and base (8 ft) are given — you're solving backwards for the height.

    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 5.3) What is the area of a trapezoid with bases 6 cm and 10 cm, and height 4 cm?

    1. A24 sq cm
    2. B32 sq cm
    3. C40 sq cm
    4. D64 sq cm

    Hint A trapezoid has two bases (6 cm and 10 cm) plus a height (4 cm) — all three belong in the formula.

    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?

Explain your thinkingIf you copied this trapezoid, flipped it, and placed it next to the original, what shape would you get? How does this help you find the area?

Sentence starter The area of the trapezoid is 1/2 x (___ + ___) x ___ = 1/2 x ___ x ___ = ___ square feet.

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