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

Lesson 5.4Composite Figures

Apply Day · Set BSecond form · new problems, same idea

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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.

Remember5.4 · Part II

Area of Composite Figures

  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. 1Complete each step, then write the final answer.

    A shape is made of a 4 ft by 2 ft rectangle joined to a 2 ft by 2 ft square. Find its total area.

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.
    6 ft10 ft8 ft

    A house shape is a 10 ft by 8 ft rectangle with a triangle on top. The triangle has a base of 10 ft and a height of 6 ft. Find the total area.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    An L-shaped garden has a bottom side of 14 ft and a left side of 10 ft. The top side is 8 ft. The short right side is 6 ft. Find the area.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    A yard is a rectangle 20 m by 15 m. A square pool is in the yard. Each side of the pool is 6 m. The rest of the yard is grass. How much of the yard is grass?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A window is a regular octagon. It splits into 8 congruent triangles. Each has a base of 10 inches and a height of 12 inches. Find the area of the window.

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    A square tile is 12 cm on each side. A triangle is cut from each of its 4 corners. Each triangle has a base of 3 cm and a height of 3 cm. What area is left?

    Show your work
    Final answer:
  7. 7Circle the letter of the best answer. Show how you know.

    An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?

    1. A12 sq ft
    2. B60 sq ft
    3. C72 sq ft
    4. D72 ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  8. 8Circle the letter of the best answer. Show how you know.

    A rectangular patio is 15 ft × 10 ft with a 5 ft × 4 ft rectangular flower bed cut out. What is the remaining area?

    1. A20 sq ft
    2. B130 sq ft
    3. C150 sq ft
    4. D170 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  9. 9Circle the letter of the best answer. Show how you know.

    Find the area of an L-shape made of a 5×3 rectangle and a 2×4 rectangle.

    1. A8 sq units
    2. B15 sq units
    3. C20 sq units
    4. D23 sq units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
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