Polygon - Types

Grade 10 · Mathematics

Semester 2 | Period 6 | Week 31

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Subject: Mathematics

Semester: 2

Period: 6

Week: 31

Week 31
Class: Grade 10
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Polygon – Types

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Identify different types of polygons based on the number of sides.
  2. Derive and use the formula for the sum of interior angles of any n-sided polygon.
  3. State and use the formula for the sum of exterior angles of any polygon.
  4. Solve numerical problems involving interior and exterior angles.
  5. Distinguish between regular and irregular polygons.

INSTRUCTIONAL TECHNIQUES:

  • Explanation and illustration
  • Question and answer
  • Guided discovery
  • Problem-solving approach
  • Real-life connections

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Chart showing types of polygons
  • Protractors, rulers
  • Polygon models (cut-outs)
  • Worksheets for exercises

 

PERIOD 1 & 2: Introduction to Polygons and Angle Sums

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of polygons and classifies them based on number of sides (triangle, quadrilateral, pentagon, etc.).

Students listen and list examples.

Step 2 - Interior Angles

Derives the formula for the sum of interior angles: (n – 2) × 180°. Works examples using triangle, quadrilateral, and hexagon.

Students follow derivation and practice examples.

Step 3 - Exterior Angles

Explains the concept of exterior angles and the formula: sum = 360°. Demonstrates with diagrams.

Students listen and draw illustrations.

Step 4 - Regular Polygons

Explains regular vs. irregular polygons and demonstrates how to calculate individual interior and exterior angles in regular polygons.

Students calculate and note angles of regular polygons.

Step 5 - Application

Solves problems involving the number of sides given the sum of interior angles or individual angle values.

Students attempt similar problems in their notebooks.

NOTE ON BOARD:

  • Sum of interior angles = (n – 2) × 180°
  • Sum of exterior angles of any polygon = 360°
  • Regular polygon: All sides and angles equal

 

EVALUATION (5 exercises):

  1. What is the sum of the interior angles of a hexagon?
  2. Find the measure of each exterior angle of a regular octagon.
  3. How many sides does a polygon have if its interior angles sum to 1,440°?
  4. What is a regular polygon? Give two examples.
  5. Find the measure of each interior angle in a regular pentagon.

CLASSWORK (5 questions):

  1. Classify polygons with 3, 4, 5, 6, 8, and 10 sides.
  2. Calculate the sum of interior angles in a decagon.
  3. Determine the number of sides in a polygon where each interior angle is 150°.
  4. Find the exterior angle of a regular dodecagon.
  5. Distinguish between regular and irregular polygons using diagrams.

ASSIGNMENT (5 tasks):

  1. Research and list real-life objects that resemble regular polygons.
  2. Solve: What is the sum of the interior angles of a 20-sided polygon?
  3. Draw and label any three regular polygons and find their angle measures.
  4. Write two uses of polygons in everyday life.
  5. Design a mini chart showing polygons from 3 to 12 sides with names and diagrams.

 

PERIOD 3 & 4: Guided Practice and Problem Solving

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review

Reviews definitions and angle formulas. Uses questioning to assess prior understanding.

Students answer review questions and take notes.

Step 2 - Guided Practice

Solves examples on the board involving unknown sides or angles of polygons.

Students solve similar problems in pairs or groups.

Step 3 - Problem Solving

Gives complex word problems involving interior and exterior angles. Guides students step-by-step.

Students work on problems and present solutions.

Step 4 - Class Discussion

Leads discussion on mistakes and challenges faced in problem solving.

Students share difficulties and ask questions.

Step 5 - Extension

Challenges students with questions involving both interior and exterior angles.

Students attempt exercises individually.

NOTE ON BOARD:

  • Use angle formulas to solve for missing variables
  • Regular polygon: all interior angles equal
  • Exterior angle = 360° ÷ number of sides

 

EVALUATION (5 exercises):

  1. Find the number of sides in a polygon if one exterior angle is 24°.
  2. What is each interior angle of a regular 12-sided polygon?
  3. Solve: A polygon has an interior angle of 162°, how many sides does it have?
  4. Differentiate between convex and concave polygons.
  5. How many diagonals can be drawn in a 9-sided polygon? (Bonus)

CLASSWORK (5 questions):

  1. Draw a heptagon and label its angles.
  2. Find the sum of interior angles in an 18-gon.
  3. Determine each interior angle of a regular hexagon.
  4. Calculate each exterior angle of a regular decagon.
  5. Solve: If the sum of interior angles is 900°, how many sides?

ASSIGNMENT (5 tasks):

  1. Create a table for polygons from 3 to 10 sides with their angle sums.
  2. Find the measure of each angle in a regular nonagon.
  3. Explain how polygons are used in tiling or mosaic designs.
  4. Draw and label a convex and a concave polygon.
  5. Write short notes on three types of polygons with real-life examples.

 

PERIOD 5: Conclusion and Review

PRESENTATION:

  • Recap key concepts on polygon types and angle formulas.
  • Display a polygon chart and ask quick questions on classification and angle rules.
  • Solve 2–3 wrap-up problems on the board.
  • Answer students’ remaining questions and give learning tips.

 

EVALUATION:

  1. Rapid questions on polygon names, angle formulas, and real-life examples.
  2. Review and correct students’ classwork and assignments.
  3. Offer feedback and encourage further independent study on the topic.