Geometric Figures and Polygons

Grade 6 · Mathematics

Semester 2 | Period 5 | Week 28

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Subject: Mathematics

Semester: 2

Period: 5

Week: 28

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 28
Lesson Duration: 45 minutes
Week & Period: Week 28, Period 5
Topic: Geometric Figures and Polygons
Sub-topic: Properties, Perimeter, and Area

Learning Objectives
By the end of the lesson, students should be able to:
Define polygons and give examples
State properties of triangles, rectangles, and squares
Calculate perimeter and area of 2D figures
Measure circumference and area of circles

Previous Knowledge
Students already know lines, angles, and simple shapes.

Instructional Materials
Mathematics textbook for Grade 6

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher displays cut-outs of a triangle, square, and rectangle. Learners name each shape.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definitions and Explanations

  1. Polygon
  • A polygon is a closed two-dimensional figure formed by straight line segments (not curves).
  • Each line segment is called a side, and the meeting points are called vertices.
  • Examples: triangle, square, rectangle, pentagon, hexagon.
  1. Examples of Polygons
  • Triangle → 3 sides
  • Square → 4 equal sides, 4 right angles
  • Rectangle → 4 sides with opposite sides equal and 4 right angles
  • Pentagon → 5 sides
  • Hexagon → 6 sides
  1. Properties of Basic Polygons
  • Triangle: 3 sides, 3 angles, sum of angles = 180°.
  • Square: 4 equal sides, 4 equal angles (90° each).
  • Rectangle: Opposite sides equal, 4 right angles.
  • Parallelogram: Opposite sides parallel and equal.
  • Trapezium: One pair of parallel sides.

 

Perimeter

  • Definition: The perimeter is the distance around a polygon — i.e., the sum of the lengths of all its sides.

Examples:

  1. Square with side 5 cm → Perimeter = 4 × 5 = 20 cm.
  2. Rectangle with length 8 cm, breadth 6 cm → Perimeter = 2(l + b) = 2(8 + 6) = 28 cm.
  3. Triangle with sides 3 cm, 4 cm, and 5 cm → Perimeter = 3 + 4 + 5 = 12 cm.

Area

  • Definition: The area is the amount of surface a shape covers, measured in square units (cm², m²).

Formulas and Examples:

  1. Square → Area = l × l.
    • Example: side = 6 cm → Area = 6 × 6 = 36 cm².
  2. Rectangle → Area = l × b.
    • Example: l = 10 cm, b = 4 cm → Area = 10 × 4 = 40 cm².
  3. Triangle → Area = ½ × base × height.
    • Example: base = 8 cm, height = 6 cm → Area = ½ × 8 × 6 = 24 cm².

 

Circle

  1. Parts of a Circle
  • Radius (r): Distance from center to any point on the circle.
  • Diameter (d): Distance across the circle through the center (d = 2r).
  • Circumference (C): Distance around the circle.
  • Area (A): Surface enclosed by the circle.
  1. Formulas:
  • Circumference = 2πr (take π = 3.14 or 22/7).
  • Area = πr².

Example:

  • Circle with r = 7 cm.
    • Circumference = 2 × 22/7 × 7 = 44 cm.
    • Area = 22/7 × 7 × 7 = 154 cm².

Worked Problems

  1. Find the perimeter of a rectangle with length = 15 cm, breadth = 10 cm.
    • P = 2(l + b) = 2(15 + 10) = 50 cm.
  2. Find the area of a square with side = 12 cm.
    • A = l × l = 12 × 12 = 144 cm².
  3. A triangle has base = 10 cm and height = 9 cm. Find its area.
    • A = ½ × 10 × 9 = 45 cm².
  4. A circle has radius = 14 cm. Find its circumference and area.
    • C = 2 × 22/7 × 14 = 88 cm.
    • A = 22/7 × 14 × 14 = 616 cm².

 

Learners’ Activities (Expanded)

  • Learners draw and label polygons (triangle, rectangle, square, pentagon) in exercise books.
  • Learners measure the sides of their polygons using rulers and calculate perimeters.
  • Learners solve area problems in pairs (given sides, find area).
  • Learners draw circles using compasses, label radius and diameter, then calculate circumference and area.
  • Learners participate in a “polygon game” where teacher names a shape and learners quickly sketch it.

 

Assessment Checks

  1. Define polygon. Give two examples.
  2. A rectangle has length = 9 cm and breadth = 4 cm. Find:
    Its perimeter
    ii. Its area
  3. Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.
  4. Find the area of a square with side 7 cm.
  5. A circle has radius 3.5 cm. Find its circumference and area (use π = 22/7).

 

Notes (Expanded & Detailed)

  • A polygon is a closed figure with straight sides.
  • Perimeter measures boundary length, Area measures surface covered.
  • Squares and rectangles are examples of quadrilaterals.
  • Triangles are the simplest polygons, and their area uses base and height.
  • The circle is a special figure defined by its radius. It has no straight sides.
  • Formulas must always be memorized and applied correctly.
  • Geometry has many real-life uses: building design, land measurement, fencing, tiling, and wheel design.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reminds learners of formulas for area and perimeter.

Evaluation Method (Expanded):
Exit slip/quiz: Find perimeter of rectangle with l = 12 cm, b = 5 cm. Teacher will collect slips and provide oral feedback.

Assignment (Expanded):
Find area of: square side 8 cm, triangle base 10 cm height 5 cm, circle radius 14 cm.

Follow-up Activity:
Learners measure objects at home (doors, tables) and calculate perimeter and area.

Differentiation / Inclusive Strategies
Provide formula charts for learners who need support. Use hands-on group activity for learners needing reinforcement.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low