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

Second Practice Form · Independent Application and Spiral Review

Area of Regular Polygons · Regular Polygon

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■ ADVANCED CONCEPT ANCHOR: 5.9 · Part II
1Area of Regular Polygons
2The Structural Procedure
  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).
  1. 1 MULTIPLE CHOICE

    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?

    1. A168 square centimeters
    2. B28 square centimeters
    3. C56 square centimeters
    4. D336 square centimeters
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2 MULTIPLE CHOICE

    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. A15.6 sq ft
    2. B31.2 sq ft
    3. C11.2 sq ft
    4. D15.6 ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3 MULTIPLE CHOICE

    Using the triangle from the previous question, what is the total area of the hexagonal skylight?

    1. A93.6 sq ft
    2. B15.6 sq ft
    3. C187.2 sq ft
    4. D62.4 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  4. 4 MULTIPLE CHOICE

    A regular hexagon is split into 6 triangles, each with base 4 cm and height 3.5 cm. What is the total area?

    1. A42 sq cm
    2. B21 sq cm
    3. C84 sq cm
    4. D14 sq cm
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It