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

Lesson 5.4Apply Area Concepts to Solve Problems

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 composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas.

Why This Matters Your architecture firm is calculating the floor area of an L-shaped room for a client's new home. The contractor needs the total area to order the correct amount of flooring. The room can be split into two rectangles: one is 12 feet by 8 feet and the other is 6 feet by 5 feet.

RememberApply Area Concepts to Solve Problems

Area of Composite Figures A composite figure is a shape made of two or more simple shapes joined together. We decompose it into basic shapes, find each area, then add or subtract.

  1. Decompose: Split the irregular shape into basic figures (rectangles, triangles, trapezoids).
  2. Calculate: Find the area of each individual sub-figure.
  3. Combine: Add the areas together (or subtract if a piece is removed/cut out)

Words: Composite Figure (Figura compuesta)Decompose (Descomponer)Add (Sumar)Subtract (Restar)Formula (Fórmula)

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

    In the formula A = ½(b₁ + b₂) × h, what do b₁ and b₂ stand for?

    1. AThe two slanted sides
    2. BThe base and the height
    3. CThe perimeter and the height
    4. DThe two parallel sides
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    What is the area of a trapezoid with bases 6 cm and 10 cm and height 4 cm?

    1. A20 square cm
    2. B32 square cm
    3. C64 square cm
    4. D240 square cm
    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 trapezoid with bases 5 cm and 9 cm and height 6 cm?

    1. A20 square cm
    2. B42 square cm
    3. C84 square cm
    4. D270 square cm
    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.

    A trapezoid has an area of 30 square feet with bases of 4 ft and 8 ft. What is its height?

    1. A2.5 feet
    2. B5 feet
    3. C6 feet
    4. D10 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?
  5. 5Circle the letter of the best answer. Show how you know.

    An architect is ordering carpet for a T-shaped conference room. The top of the T is 14 feet by 4 feet and the stem is 6 feet by 10 feet. Carpet costs $5 per square foot. What is the area of the top of the T?

    1. A18 sq ft
    2. B36 sq ft
    3. C56 sq ft
    4. D60 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.

    An architect is ordering carpet for a T-shaped conference room. The top of the T is 14 feet by 4 feet and the stem is 6 feet by 10 feet. Carpet costs $5 per square foot. What is the total area of the T-shaped room?

    1. A96 sq ft
    2. B104 sq ft
    3. C116 sq ft
    4. D840 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?

Explain your thinkingFor the U-shaped pool, why did we subtract instead of add? When do you add areas and when do you subtract?

Sentence starter I ___ the areas because the composite figure is made by ___ a piece from a larger shape, so the total area is ___ - ___ = ___ square feet.

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 5.4Apply Area Concepts to Solve Problems

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 composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas.

Why This Matters Your architecture firm is calculating the floor area of an L-shaped room for a client's new home. The contractor needs the total area to order the correct amount of flooring. The room can be split into two rectangles: one is 12 feet by 8 feet and the other is 6 feet by 5 feet.

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

    Plan 3 — Survey the site. Drag each part of a floor plan into the correct group: do you ADD it to the total or SUBTRACT it from a larger shape?

    Groups: ADD to the total SUBTRACT from a larger shape
    • Triangular entrance canopy joined to the front wall
    • Square skylight opening cut out of the roof
    • Rectangular wing attached to the main hall
    • Elevator shaft removed from the office floor
    • Triangular gable joined on top of the rectangular wall
    • Circular fountain basin carved out of the courtyard
  2. 2Write the letter of the matching item on each line.

    Plan 5 — Match each floor plan to its correct total area.

    1. House-front wall: 11x6 rectangle + triangle base 11, height 4
    2. T-shaped studio: 13x4 top + 5x9 stem
    3. Warehouse 20x9 minus loading bay 6x5
    4. L-shaped gallery: 7x7 + 4x6
    • A88 sq ft
    • B97 sq ft
    • C150 sq ft
    • D73 sq ft
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    An architect is ordering carpet for a T-shaped conference room. The top of the T is 14 feet by 4 feet and the stem is 6 feet by 10 feet. Carpet costs $5 per square foot. What will the carpet cost?

    1. A$116
    2. B$300
    3. C$580
    4. D$1,160
    per 1
  2. 4Circle the letter of the best answer. Show how you know.

    A 7 ft by 5 ft rectangle has a triangle (base 7 ft, height 4 ft) on top. Add the two areas. What is the total area?

    1. A14 sq ft
    2. B35 sq ft
    3. C49 sq ft
    4. D63 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 5Circle the letter of the best answer. Show how you know.

    Plan 2 — L-shaped lobby: decompose the L into two rectangles, one 9 ft by 6 ft and one 7 ft by 3 ft, then ADD. What is the total floor area?

    1. A21 sq ft
    2. B54 sq ft
    3. C63 sq ft
    4. D75 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.

    Plan 4 — Design studio: the floor is a 16 ft by 12 ft rectangle, but a 5 ft by 4 ft storage closet is cut out of one corner. Find the usable floor area.

    1. A20 sq ft
    2. B172 sq ft
    3. C192 sq ft
    4. D212 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

Explain your thinkingFor the U-shaped pool, why did we subtract instead of add? When do you add areas and when do you subtract?

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