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

Lesson 5.1Determine the Area of Parallelograms and Rhombuses

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the area of a parallelogram using base × height.

Start hereWords for this lesson

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

WordWhat it meansExample
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. opposite sides never meet
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.
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. b in A = b × h
HeightSpanish: Altura The straight-up distance from the base to the top. h in A = b × h
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). height ⟂ base

How it worksWorked examplefinding the area of a parallelogram

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

A parallelogram has a base of 14 cm. The perpendicular height to that base is 6 cm. Find the area.

  1. Write the formula. A = b × h
  2. Name the parts. base b = 14 cm perpendicular height h = 6 cm
  3. The slanted side is never the height — use the square-corner distance.
  4. Multiply and label square units. 14 × 6 = 84

Answer: The area of the parallelogram is 84 square centimeters (84 cm²).

Now you trySame steps, your turn

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

A parallelogram has a base of 9 in. and a perpendicular height of 7 in. Find the area.

  1. Write the formula. A = ×
  2. Name the parts. base = in. height = in.
  3. Which measure makes a square corner with the base?
  4. Multiply. × = Units:
Answer:area of the parallelogram

Say it and write itSentence starters

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

  • The base is and the perpendicular height is .
  • I know that measure is the height because .
  • Area = × = square units.
  • The slanted side is not used because .

Word bank parallelogrambaseheightperpendicularsquare cornerareaformulamultiplysquare unitsslanted siderectanglerearrange

Watch outA common mistake

The most common mistake in Area of Parallelograms is multiplying the base by the slanted side instead of the perpendicular height. For a parallelogram with a base of 16 ft, a perpendicular height of 9 ft, and a slanted side of 11 ft, students compute 16 × 11 = 176 square feet instead of the correct 16 × 9 = 144 square feet. The height must be the straight-up (perpendicular) distance between the base and its opposite side, not the length of the slanted side, even though the slanted side is often the number that 'looks' like it belongs in the formula.

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

Lesson 5.1Determine the Area of Parallelograms and Rhombuses

Version ASupported practice

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

Learning target I can find the area of a parallelogram using base × height.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Use the formula A = b × h to find the area of each parallelogram.

    ParallelogramBaseHeightArea
    Patio X6 ft4 ft
    Patio Y11 ft3 ft

    Hint Each row gives a base and a height in feet — the empty Area column is what you fill in.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    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. 3Circle the letter of the best answer. Show how you know.

    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. 4Circle the letter of the best answer. Show how you know.

    What is the area of a parallelogram with base 9 cm and height 5 cm?

    1. A14 sq cm
    2. B22.5 sq cm
    3. C45 sq cm
    4. D90 sq cm

    Hint Spot the base (9 cm) and the height (5 cm). Which operation does the area formula use on them?

    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. 5Circle the letter of the best answer. Show how you know.

    Which measurement is the height of a parallelogram?

    1. AThe length of the slanted side
    2. BThe perimeter divided by 4
    3. CThe perpendicular distance between the base and the opposite side
    4. DThe longest side

    Hint Picture a leaning parallelogram. The height is not a side you can trace — it's a distance measured straight across.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Read the parallelogrambase = 7 ft, height = 4 ft
    2. 2Write the formulaA = base × height
    3. 3Substitute the valuesA = 7 + 4
    4. 4Calculate the areaA = 11 sq ft

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Look at the substitution step. Did the student add the base and height, or multiply them?

    Correct work
    Correct answer:

Explain your thinkingIf you cut a triangle from one side of the parallelogram and move it to the other side, what shape do you get? How does this help you find the area?

Sentence starter The area of the parallelogram equals base x height = ___ x ___ = ___ square feet, which is the same as a ___ with the same base and height.

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 5.1Determine the Area of Parallelograms and Rhombuses

Version BCore practice

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

Learning target I can find the area of a parallelogram using base × height.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the table.

    ParallelogramBaseHeightArea
    Patio A14 ft9 ft
    Patio B8 ft56 sq ft
    Patio C12 ft96 sq ft
    Patio D15 ft6 ft
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each shape to its area.

    1. Triangle 8×6
    2. Parallelogram 5×4
    3. Rectangle 7×3
    4. Triangle 10×8
    5. Square side 6
    6. Parallelogram 9×2
    • A24 sq units
    • B20 sq units
    • C21 sq units
    • D40 sq units
    • E36 sq units
    • F18 sq units
  3. 3Write the name of the correct group on each line.

    Sort each parallelogram by whether its area is greater than 50 sq units or 50 or less.

    Groups: Area > 50 sq units Area ≤ 50 sq units
    • b = 12, h = 5
    • b = 7, h = 6
    • b = 10, h = 8
    • b = 9, h = 4
    • b = 11, h = 7
    • b = 5, h = 10
  4. 4Mark and label each value on the number line.

    Find the missing height: b = 8, A = 48

    012345678910
    Show your thinking
Part 2Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Read the parallelogrambase = 9 cm, slanted side = 10 cm, height = 6 cm
    2. 2Write the formulaA = base × height
    3. 3Substitute the valuesA = 9 × 10
    4. 4Calculate the areaA = 90 sq cm

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingIf you cut a triangle from one side of the parallelogram and move it to the other side, what shape do you get? How does this help you find the area?

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 5.1Determine the Area of Parallelograms and Rhombuses

ChallengeExtension

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

Learning target I can find the area of a parallelogram using base × height.

Part 1Understand the ideamodels and meaning
  1. 1Plot and label each point on the grid.

    Plot the parallelogram and find its area.

    02468101214012345678unitsunits
    Show your thinking
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Area Error

    1. 1Identify base and heightb = 11 m, slant side = 8 m, h = 6 m
    2. 2Write the formulaA = b × h
    3. 3Substitute valuesA = 11 × 8
    4. 4CalculateA = 88 sq m

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A parallelogram has a base of 12 cm. If you double the height, the area doubles too. Explain why this happens using the formula, and give a specific example with numbers.

    Write your answer

Explain your thinkingIf you cut a triangle from one side of the parallelogram and move it to the other side, what shape do you get? How does this help you find the area?

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