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

Lesson 5.95.9 · Part II

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Regular PolygonSpanish: Polígono regular A closed flat shape made of straight sides, where every side is the same length and every angle is the same size. A stop sign is a regular octagon — all 8 sides are the same length and all 8 angles are equal
DecomposeSpanish: Descomponer To break a shape into smaller, simpler shapes. Draw lines from the center of a hexagon to each corner → you get 6 equal triangles you can find the area of
TriangleSpanish: Triángulo A shape with three sides. Each triangle inside a decomposed hexagon has a base = one side of the hexagon and height = distance from center to side
CompositeSpanish: Compuesto Made by putting two or more simple shapes together. 6 triangles, each with area 15 sq ft, combine to form a hexagon with total area = 6 × 15 = 90 sq ft
FormulaSpanish: Fórmula A math rule written with symbols. For a regular hexagon: Total Area = 6 × (½ × b × h), where b = side length and h = height of each triangle

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

Word bank Regular PolygonDecomposeTriangleCompositeFormula

Watch outA common mistake

A common mistake in Area of Regular Polygons is stopping after finding the area of ONE triangle and reporting that as the total area — or adding the number of triangles instead of multiplying. Remember: total area = (one triangle's area) × (number of sides), not (one triangle's area) + (number of sides).

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

Lesson 5.95.9 · Part II

Apply Day · Version ASupported practice

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

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

  1. 1Complete each step, then write the final answer.
    1 of 45 m10 m

    A square splits into 4 equal triangles from its center. Each triangle has a base of 10 m and a height of 5 m. Find the area.

    Show your work

    Hint Find one triangle: half of base × height. Then multiply by 4.

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

    A regular octagon splits into 8 equal triangles. Each triangle has a base of 2 in and a height of 2.4 in. Estimate the area.

    Show your work

    Hint Find one triangle. Then multiply by 8.

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

    A regular pentagon splits into 5 equal triangles. Each triangle has a base of 2 cm and a height of 1.4 cm. Estimate the area.

    Show your work

    Hint One triangle is half of 2 × 1.4. There are 5 triangles.

    Final answer:
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 5.95.9 · Part II

Apply Day · Version BCore practice

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

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

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

    Leo finds the area of a regular hexagon with sides of 3 cm. Each center triangle has a height of 2.6 cm. He writes 6 × 3 × 2.6 = 46.8. What is the correct area?

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

    A regular heptagon has 7 sides of 4 m. Each center triangle has a height of 4.2 m. Estimate its area.

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

    A regular decagon has 10 sides of 2 cm. Each center triangle has a height of 3.1 cm. Estimate the area.

    Show your work
    Final answer:
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 5.95.9 · Part II

Apply Day · ChallengeExtension

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

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

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

    A regular hexagon is decomposed from its center into 6 identical triangles. Each triangle has a base of 8 cm and a height of 7 cm. What is the area of the hexagon? Use the given rounded height to estimate the area.

    1. A28 square centimeters
    2. B56 square centimeters
    3. C168 square centimeters
    4. D336 square centimeters
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2Complete each step, then write the final answer.

    A regular hexagon has sides of 14 cm. Each center triangle has a height of 12.1 cm. Ana finds perimeter × height ÷ 2. Ben finds one triangle and multiplies by 6. What area do they get?

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

    A regular octagon has sides of 8 in. Its area is about 310.4 square inches. Find the height of each center triangle.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help