Project 3 : Triangulation and Interior angles of a Polygon

Project 3 : Triangulation and Interior angles of a Polygon

Exploring Interior Angles of Polygons

Class: VIII

Objective:

To discover the sum of interior angles of polygons without using direct formulae.
To explore and apply different triangulation techniques on various polygons.
To connect geometry with real-world structures and patterns.

Materials Required:

Colored paper
Scissors
Glue
Pre-printed polygon templates

Project Guidelines:

1. Polygon Selection:

Choose a minimum of 4 regular and 4 irregular polygons.
Include both convex and concave types.
Each polygon must have a unique number of sides.

2. Triangulation:

Use two triangulation techniques to divide each polygon into triangles:

Fixed Vertex Method: All triangles originate from a single chosen vertex.
Piece-wise Method: Triangles are formed by connecting non-adjacent vertices across the polygon.

Use both methods at least once among your polygons.

3. Calculating Interior Angles:

Apply the fact that each triangle’s angle sum is 180° to compute the interior angle sum of each polygon.
For regular polygons, divide the total angle sum by the number of sides to find the measure of each angle.

4. Real-Life Application:

Identify and photograph one real-world example of a polygon (e.g., tiles, windows, traffic signs).
Determine and record:

The total interior angle sum.
The individual interior angle if it's a regular polygon.

5. Tessellation Design:

Select three different polygons.
Combine them to create an aesthetically pleasing pattern.
Extend this pattern into a tessellation design.

Presentation Format:

You may present the project in either a physical format (handmade charts, models) or a digital format (PowerPoint, Canva, Google Slides, etc.).
All research and preparation must be done during the summer break. The project would be compiled and completed in school after the holidays.

Important Reminders:

Use distinct colors for different polygons to ensure clarity.
Clearly label all sides, angles, and triangulation lines.
Indicate the triangulation method used for each polygon.
Maintain neatness, originality, and clarity.
Include sources/references (books, websites, etc.) used for research.

⚠️ Important: Do not use ChatGPT or any other AI tools to generate your write-up. Your submissions will be reviewed for originality.

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