Learn on PengiReveal Math, Course 1Module 8: Area

8-4 Area of Regular Polygons

In this Grade 6 lesson from Reveal Math, Course 1, Module 8, students learn how to find the area of a regular polygon by decomposing it into congruent triangles, parallelograms, or trapezoids, calculating each smaller figure's area, and then adding or multiplying to find the total. The lesson introduces the term "regular polygon" and applies the decomposition strategy to real-world shapes like octagons and hexagons using the trapezoid and triangle area formulas.

Section 1

Definition of a Regular Polygon

Property

A regular polygon is a flat shape where all sides are the exact same length (congruent sides) and all inside angles are the exact same size (congruent angles).

Examples

  • A square is a regular quadrilateral because all four of its sides are equal and all four of its angles are exactly 90 degrees.
  • An equilateral triangle is a regular polygon because it has three equal sides and three equal angles of 60 degrees.
  • A standard rectangle is NOT a regular polygon. Even though its angles are all equal (90 degrees), its adjacent sides are different lengths.

Explanation

A regular polygon is the superstar of the shape world! Imagine a shape where everything is perfectly balanced and fair. No side is longer and no corner is wider—it is pure geometric harmony. Whenever you see the word "regular" in geometry, just think: "Perfectly equal in every way."

Book overview

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Module 8: Area

  1. Lesson 1

    8-1 Area of Parallelograms

  2. Lesson 2

    8-2 Area of Triangles

  3. Lesson 3

    8-3 Area of Trapezoids

  4. Lesson 4Current

    8-4 Area of Regular Polygons

  5. Lesson 5

    8-5 Polygons on the Coordinate Plane

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Definition of a Regular Polygon

Property

A regular polygon is a flat shape where all sides are the exact same length (congruent sides) and all inside angles are the exact same size (congruent angles).

Examples

  • A square is a regular quadrilateral because all four of its sides are equal and all four of its angles are exactly 90 degrees.
  • An equilateral triangle is a regular polygon because it has three equal sides and three equal angles of 60 degrees.
  • A standard rectangle is NOT a regular polygon. Even though its angles are all equal (90 degrees), its adjacent sides are different lengths.

Explanation

A regular polygon is the superstar of the shape world! Imagine a shape where everything is perfectly balanced and fair. No side is longer and no corner is wider—it is pure geometric harmony. Whenever you see the word "regular" in geometry, just think: "Perfectly equal in every way."

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 8: Area

  1. Lesson 1

    8-1 Area of Parallelograms

  2. Lesson 2

    8-2 Area of Triangles

  3. Lesson 3

    8-3 Area of Trapezoids

  4. Lesson 4Current

    8-4 Area of Regular Polygons

  5. Lesson 5

    8-5 Polygons on the Coordinate Plane