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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