6.GR.1 Lesson 5-9-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.9 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Area of Regular Polygons · Regular Polygon · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the area of a regular polygon?
1A regular polygon splits into the same number of triangles as it has sides, so total area = (one triangle's area) × (number of sides).
  • A regular polygon is a closed shape with straight sides where every side is the same length and every angle is the same size. We can decompose it (break it apart) into equal triangles from the center, then add up their areas. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. My hexagon has 6 equal sides. Each side is 6 feet, and each center triangle has a height of 5.2 feet.
  2. First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
  3. I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
  4. A hexagon has 6 sides, so it has 6 equal triangles.
  5. I multiply: 6 × 15.6 = 93.6. So the total area is 93.6 square feet.
3Mathematical Word Bank
  • Area of Regular Polygons (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.
  • Regular Polygon (Polígono regular) — A closed flat shape made of straight sides, where every side is the same length and every angle is the same size.
  • Decompose (Descomponer) — To break a shape into smaller, simpler shapes.
  • Triangle (Triángulo) — A shape with three sides.
  • Composite (Compuesto) — Made by putting two or more simple shapes together.
  • Formula (Fórmula) — A math rule written with symbols.
4Watch out
  • 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).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A regular hexagonal floor tile splits from its center into 6 congruent triangles, each with an area of 12 cm². What is the total area of the tile?

    1. A72 cm²
    2. B12 cm²
    3. C36 cm²
    4. D18 cm²
    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. 2 MULTIPLE CHOICE

    A regular pentagonal tile splits into 5 congruent triangles. Each triangle has a base of 4 in and a height of 6 in. What is the total area of the tile?

    1. A60 in²
    2. B12 in²
    3. C24 in²
    4. D120 in²
    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. 3 MULTIPLE CHOICE

    An octagon tile splits into equal triangles, each with base 6 ft and height 5 ft. How many triangles, and what is the total area?

    1. A120 sq ft
    2. B15 sq ft
    3. C90 sq ft
    4. D105 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?
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Decompose the octagon:A regular octagon = 8 congruent triangles
    2. 2Identify one triangle:base = 3 ft, height = 4 ft
    3. 3Find the area of one triangle:A = ½ × 3 × 4 = 6 sq ft
    4. 4Find total area:Total area = 5 × 6 = 30 sq ft

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Level 2 Extension — Find the Tile Area Error

    1. 1Decompose the tile:A regular hexagonal tile = 6 congruent triangles
    2. 2Identify one triangle:base = 8 in, height = 3.5 in
    3. 3Find the area of one triangle:A = ½ × 8 × 3.5 = 14 sq in
    4. 4State the total tile area:Total area = 14 sq in

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Area Error

    1. 1Decompose the hexagon:A regular hexagon = 6 triangles
    2. 2Find area of one triangle:b = 5 m, h = 4.3 m
    3. 3Calculate one triangle:A = ½ × 5 × 4.3 = 10.75 sq m
    4. 4Find total area:Total = 10.75 + 6 = 16.75 sq m

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It