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

Lesson 5.45.4 · 5.9 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 5.4 · 5.9 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Composite FigureSpanish: Figura compuesta A shape made by putting two or more simple shapes together. triangles joined together
DecomposeSpanish: Descomponer To break a shape into smaller, simpler shapes. hexagon → 6 triangles
AddSpanish: Sumar Add up the areas of the smaller shapes to get the total. T-shaped hallway: top rectangle = 30 sq ft, bottom rectangle = 28 sq ft → total = 30 + 28 = 58 sq ft
SubtractSpanish: Restar Take away the area of a missing piece from a bigger shape. A 14×10 pool with a 6×4 cutout: 140 − 24 = 116 sq ft of water surface
FormulaSpanish: Fórmula A math rule written with symbols. Rectangle: A = l × w; Triangle: A = ½ × b × h; use the right formula for each piece of a composite figure
Area of Regular PolygonsSpanish: Área de polígonos regulares The space a regular polygon covers. Split it from the center into identical triangles, find one triangle's area, then multiply by how many there are. A hexagon splits into 6 identical triangles: (½ × 4 × 3.5) × 6 = 42 square units

How it worksWorked examplearea of a regular polygon

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A regular octagon has sides of 12 in. A triangle drawn from the center to one side has a height of 14 in. Find the area.

  1. A regular octagon has eight equal sides, so it decomposes into eight congruent triangles.
  2. Find the area of ONE triangle. ½ × 12 × 14 = 84
  3. Every triangle matches, so multiply by how many there are. 84 × 8 = 672

Answer: The area of the octagon is 672 square inches (672 in²).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A regular hexagon has sides of 20 m. Each triangle drawn from the center has a height of 17 m. Find the area.

  1. How many congruent triangles does a regular hexagon decompose into?
  2. Area of ONE triangle. ½ × × =
  3. Multiply by the number of triangles. × =
Answer:area of the hexagon

Say it and write itSentence starters

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

  • I decomposed the figure into congruent .
  • The area of one triangle is square units.
  • There are triangles, so the total area is .
  • I know the triangles are congruent because .

Word bank regular polygondecomposecongruenttrianglecenterbaseheightmultiplytotalareasquare unitscomposite figure

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 5.45.4 · 5.9 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 5.4 · 5.9 by using each lesson's big idea in mixed practice.

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

    (Lesson 5.4) 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

    Hint The L-shape is already split into two rectangles for you: 10 × 6 and 4 × 3.

    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?
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 5.4) 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

    Hint The flower bed is CUT OUT of the patio — that phrase tells you which operation to use.

    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.

    (Lesson 5.9) 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?

    1. A11.2 sq ft
    2. B15.6 sq ft
    3. C15.6 ft
    4. D31.2 sq ft

    Hint Focus on just ONE of the 6 triangles: its base is 6 ft and its height is 5.2 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?
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 5.9) Using the triangle from the previous question, what is the total area of the hexagonal skylight?

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

    Hint You already found one triangle's area (15.6 sq ft) in the last question — now think about the whole hexagon.

    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 thinkingThe hexagon and the octagon both have triangles, but the totals are different. What two things decide the total area of a regular polygon?

Sentence starter The total area is ___ because one triangle is ___ and there are ___ triangles.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help