Contextualization

Polygons and diagonals are fundamental concepts in geometry that are widely used in various areas, from architecture and design to more complex fields such as engineering and physics.

At first, it may seem that the analysis of polygons and the calculation of their diagonals are isolated topics, far from everyday life. However, looking around, we will see that polygons are present everywhere: in architectural structures, works of art, furniture design, and even in nature. Understanding how these shapes work, and how they relate to their diagonals, is a fundamental mathematical skill.

Introduction

A polygon is a closed flat figure composed of straight segments, known as sides. When these sides connect, they form angles called interior angles. An interesting aspect of polygons is that they can have any number of sides, as long as it is greater than three.

The diagonal of a polygon is a straight segment that connects two non-consecutive vertices. For example, a square has two diagonals, while a pentagon has five. This relationship between the number of sides of a polygon and its diagonals is a key area of geometry and will be the main focus of this project.

To deepen the study of this fundamental topic, we recommend the following sources:

1. How to Calculate Diagonals of a Polygon
2. Polygons - Mundo Educação
3. Regular Polygon - Brasil Escola

These resources provide a solid foundation for understanding the theme of our project.

Practical Activity

Activity Title: Building and Analyzing Polygons - A Look at Diagonals

Project Objective

The objective of this project is to provide students with a practical and engaging experience with the geometry of polygons and their diagonals. The focus will be on the theoretical and practical understanding of the concept of polygon diagonals and their calculation.

Detailed Project Description

This project will be carried out in groups of 3 to 5 students, with a total estimated duration of 12 hours per student, and will involve the development of 4 key competencies:

1. Theoretical understanding of polygons and their diagonals
2. Construction of polygon models
3. Drawing and counting diagonals
4. Preparation of final report

The project's goal is that, by the end, students will be able to:

1. Identify and construct, in a practical way, polygons according to the number of sides;
2. Draw the diagonals of these polygons and understand the relationship between the number of sides and the number of diagonals;
3. Understand the concept of polygon diagonals and how to calculate this quantity.

Required Materials

1. Colored cardboard
2. Ruler
3. Compass
4. Colored pencils
5. Markers
6. Blunt scissors
7. Glue
8. Graph paper

Detailed Step-by-Step

1. Theoretical Research: Start by conducting research on polygons and diagonals in various materials such as math books and reliable websites indicated by the teacher. The goal is to understand the concept of polygons and diagonals and how to calculate the quantity of diagonals in a polygon.

2. Construction of Polygon Models: With the available materials, each group should draw and cut out models of polygons with different numbers of sides (from 3 to 7). Use colored cardboard, ruler, and compass for precision.

3. Drawing Diagonals: Next, using markers and graph paper, the groups should draw the diagonals of each of these polygons and count them.

4. Comparison and Analysis: Students should now compare the results obtained with the theoretically calculated number of diagonals.

5. Preparation of the Report: Finally, the groups should write a detailed report of their findings, describing the process they followed, the results obtained, and the conclusions reached.

Project Deliverables

At the end of the project, each group must deliver:

1. Physical Models of Polygons: Models made of colored cardboard of polygons ranging from 3 to 7 sides.

2. Drawings of Polygons with Diagonals: Drawings of the polygons with their respective diagonals on graph paper.

3. Final Report: A detailed report describing the project, the process followed, the results obtained, and the conclusions reached. The report should include:

• Introduction: In this section, students should explain what a polygon is, what diagonals are, their importance in mathematics and real life, in addition to the project's objectives.

• Development: In this section, students should describe in detail the procedure followed, from the initial research to the construction and analysis of polygons and diagonals. The results obtained should also be presented and discussed here.

• Conclusion: Here, students should summarize the main points of the work, discuss what they learned from the project, and what conclusions they were able to draw from it.

• Bibliography: In this final section of the report, students should list all the sources consulted for the project.

These deliverables allow for a comprehensive assessment of the skills acquired by students, both technical and socio-emotional, and are directly related to the practical and theoretical content worked on in the project.