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

Lesson 5.95.9 · Part II

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

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Learning target I can find the area of a regular polygon by decomposing it into triangles.

Remember5.9 · Part II

Area of Regular Polygons

  1. Decompose the regular polygon from center into n congruent triangles
  2. Find the area of one triangle using A = ½ × side × apothem (height)
  3. Multiply by the total number of sides

Words: Regular Polygon (Polígono regular)Decompose (Descomponer)Triangle (Triángulo)Composite (Compuesto)Formula (Fórmula)

  1. 1Complete each step, then write the final answer.
    1 of 43 cm6 cm

    A square has sides of 6 cm. Lines from its center split it into 4 equal triangles. Each triangle has a height of 3 cm. Find the area using the triangles.

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

    A regular pentagon has sides of 8 in. Each center triangle has a height of 5.5 in. Estimate the area of the pentagon.

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

    A regular polygon is made of equal center triangles. Each triangle has a base of 6 in and a height of 7.2 in. The area is about 172.8 square inches. How many sides does it have?

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

    A floor tile is a regular hexagon. Each side is 2 in. Each center triangle has a height of 1.7 in. About how much floor does one tile cover?

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

    A pool cover is a regular pentagon with sides of 6 ft. Each center triangle has a height of 4.1 ft. The cover costs $2 for each square foot. About how much does it cost?

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

    A regular hexagon and a regular pentagon each have a perimeter of 120 cm. The hexagon's center triangles have a height of 17.3 cm. The pentagon's have a height of 16.5 cm. Which has more area? How much more?

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

    A regular hexagon is divided into 6 equal triangles from the center. Each triangle has a base of 6 ft and a height of 5.2 ft. What is the area of one triangle? Use the given heights; nonsquare heights are rounded, so their areas are estimates.

    1. A11.2 sq ft
    2. B15.6 sq ft
    3. C15.6 ft
    4. D31.2 sq 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 regular hexagonal skylight has 6 central triangles, each with base 6 ft and rounded height 5.2 ft. Using those measurements, what is the approximate total area?

    1. A15.6 sq ft
    2. B62.4 sq ft
    3. C93.6 sq ft
    4. D187.2 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.

    A regular hexagon is split into 6 triangles, each with base 4 cm and height 3.5 cm. What is the total area? Use the given heights; nonsquare heights are rounded, so their areas are estimates.

    1. A14 sq cm
    2. B21 sq cm
    3. C42 sq cm
    4. D84 sq cm
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
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