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.

Why This Matters Your architecture firm is designing a parallelogram-shaped patio for a client's backyard. The client needs to know how many square feet of pavers to order. The patio has a base of 14 feet and a height of 9 feet.

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 example

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

Base 9 in., height 4 in., slanted side 5 in. Find the area.

  1. Base = 9 in., height = 4 in.
  2. Skip the 5 in. slanted side.
  3. A = 9 × 4 = 36

Answer: 36 in²

Now you trySame steps, your turn

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

Now a smaller parallelogram: base = 5 cm, height = 4 cm.

Answer:

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 out!A 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

Level 0Most support · every hint printed

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

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

Why This Matters Your architecture firm is designing a parallelogram-shaped patio for a client's backyard. The client needs to know how many square feet of pavers to order. The patio has a base of 14 feet and a height of 9 feet.

How it worksWorked example

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

Base 9 in., height 4 in., slanted side 5 in. Find the area.

  1. Base = 9 in., height = 4 in.
  2. Skip the 5 in. slanted side.
  3. A = 9 × 4 = 36

Answer: 36 in²

  1. 1Circle 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
    Steps to try
    1. You know both the base (10 cm) and the height (7 cm) — this is a direct use of the parallelogram area formula.
    2. Area of a parallelogram is A = base × height. Adding the two numbers gives perimeter-style thinking, not area.
    3. Set up A = 10 × 7 and multiply. Label your result in square centimeters.
    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.

    A parallelogram patio on the firm's blueprint 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
    Steps to try
    1. This time you're given the area (54 sq ft) and the base (9 ft) — the height is the missing piece.
    2. Start from A = b × h. To undo a multiplication, divide: h = A ÷ b.
    3. Write 54 = 9 × h, then divide 54 by 9 to find the height in feet.
    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.

    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
    Steps to try
    1. Spot the base (9 cm) and the height (5 cm). Which operation does the area formula use on them?
    2. Use A = base × height. If your number looks like 9 + 5, or like half the product, rethink the operation.
    3. Compute 9 × 5 and give the answer in square centimeters.
    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.

    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
    Steps to try
    1. Picture a leaning parallelogram. The height is not a side you can trace — it's a distance measured straight across.
    2. Height must make a right angle (90°) with the base. Test each choice: is this perpendicular to the base?
    3. Draw a base, then a straight up-and-down dashed line to the opposite side. That dashed line is what 'height' means here.
    Show your work

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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help