6.GR.1 Lesson 5-9-part2 Apply Day · Practice
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5.9 · Part II

Application Practice for Today's Problem

Area of Regular Polygons · Regular Polygon

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.9 · Part II
1Area of Regular Polygons
2Strategy Model — step by step
  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
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

    How many triangles can you make from the center of a regular pentagon?

    1. A5
    2. B3
    3. C6
    4. D10
    ✏️ Workspace & Solution Steps
  2. 2 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?
  3. 3 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?
  4. 4 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. 5 OPEN RESPONSE

    A regular hexagon and a regular pentagon both have triangles with the same base (6 ft) and the same height (5 ft). Which polygon has the greater total area? Explain why the number of sides matters.

    💬 Sentence Starter: One triangle's area is ½ × ___ × ___ = ___. The hexagon has ___ triangles so its area is ___. The pentagon has ___ triangles so its area is ___. The ___ has more area because ___.
    ✏️ Mathematical Justification & Response
📐 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