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

Lesson 5.1Determine the Area of Parallelograms and Rhombuses

Set B · Version ASecond form · supported practice

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.

RememberDetermine the Area of Parallelograms and Rhombuses

Area of Parallelograms & Rhombuses. Formula: Area = Base × Height (A = b · h) A parallelogram is a four-sided shape with two pairs of parallel sides, like a leaning rectangle. Its area is how much flat space is inside it.

  1. Identify the base (any side).
  2. Identify the perpendicular height (height must be perpendicular to base, not slanted).
  3. Multiply base times height; label with square units (e.g. cm², in²)

Words: Slanted side (Lado inclinado)Parallelogram (Paralelogramo)Parallel (Paralelas)Base (Base)Height (Altura)

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

    A bus travels 45 miles each hour. Which equation gives the distance d after h hours?

    1. Ad = 45h
    2. Bd = 45 + h
    3. Cd = h ÷ 45
    4. Dd = 45 − h
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Using d = 45h, how far does the bus travel in 6 hours?

    1. A7.5 miles
    2. B45 miles
    3. C51 miles
    4. D270 miles
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  3. 3Circle the letter of the best answer. Show how you know.

    A table shows x = 1, 2, 3 with y = 6, 12, 18. Which equation fits?

    1. Ay = x + 5
    2. By = 6x
    3. Cy = x + 6
    4. Dy = 6 + x
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    In c = 3n, the cost c depends on the number n. Which is the dependent variable?

    1. An
    2. B3
    3. Cc
    4. DBoth of them
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A landscape architect is tiling a parallelogram-shaped courtyard. The courtyard has a base of 18 feet and a height of 10 feet. Each tile covers 2 square feet. What is the area of the parallelogram courtyard?

    1. A28 sq ft
    2. B56 sq ft
    3. C90 sq ft
    4. D180 sq ft
    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?
  6. 6Circle the letter of the best answer. Show how you know.

    A landscape architect is tiling a parallelogram-shaped courtyard. The courtyard has a base of 18 feet and a height of 10 feet. Each tile covers 2 square feet. How many tiles does the architect need?

    1. A45
    2. B90
    3. C180
    4. D360
    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
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.1Determine the Area of Parallelograms and Rhombuses

Set B · Version BSecond form · core practice

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.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Each label describes a segment on a parallelogram blueprint. Sort each one into 'Is the height' or 'Is NOT the height'.

    Groups: Is the height Is NOT the height
    • A dashed line straight up from the base, making a 90 degree angle
    • The slanted left edge of the parallelogram
    • The perpendicular distance from the base to the top side
    • The long tilted side that connects the bottom to the top
    • The straight-up distance measured at a right angle to the base
    • The leaning side that is longer than the perpendicular gap
  2. 2Write the letter of the matching item on each line.

    Match each parallelogram's base and height to its correct area (A = base x height).

    1. base 6 ft, height 7 ft
    2. base 13 ft, height 2 ft
    3. base 4 ft, height 11 ft
    4. base 15 ft, height 4 ft
    • A42 sq ft
    • B26 sq ft
    • C44 sq ft
    • D60 sq ft
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A landscape architect is tiling a parallelogram-shaped courtyard. The courtyard has a base of 18 feet and a height of 10 feet. Each tile covers 2 square feet. Why use the height instead of the slanted side length?

    1. ABecause the slanted side is always longer
    2. BBecause parallelograms have no height
    3. CBecause the base is on the bottom
    4. DBecause area needs the perpendicular distance between the two bases
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Cut the slanted end off a parallelogram and slide it to the other side. What shape forms, and why does that show A = base × height?

    1. AA bigger parallelogram, so the area gets larger
    2. BA triangle, so the area is cut in half
    3. CA square, so all four sides must be equal
    4. DA rectangle with the same base and height, so its area equals base x height
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    A blueprint parallelogram has a base of 8 ft, a height of 5 ft, and a slanted side of 7 ft. What is its area?

    1. A26 sq ft
    2. B35 sq ft
    3. C40 sq ft
    4. D56 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  4. 6Circle the letter of the best answer. Show how you know.

    Two parallelograms both have base 10 ft and height 6 ft. N is more tilted (slant 9 ft). Compare their areas.

    1. ABlueprint N is larger because its slanted side is 9 ft
    2. BBlueprint M is larger because it is less tilted
    3. CEqual: both are 10 x 6 = 60 sq ft because area depends on base and height, not the slant
    4. DYou cannot compare them without the slanted side of M
    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?

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