Contextualization

Regular polygons are closed figures, formed by line segments, where all sides and angles are equal. Thus, they constitute one of the fundamental elements of geometry, a subarea of mathematics that studies the properties and measurements of figures in space. This discipline, in turn, plays a vital role in developing students' ability for abstraction and logical reasoning.

There are several known regular polygons, such as the equilateral triangle, the square, the regular pentagon, and so on. Each of these polygons has its own characteristics, such as the number of diagonals passing through the center, and the values of the internal and external angles, which can be calculated through specific formulas.

Introduction

The study of regular polygons is very important because they are everywhere in the real world. Walls, tiles, floors, windows, doors, furniture, paintings, pieces of clothing, packaging, and a multitude of other objects have shapes that can be described as regular polygons or combinations of these.

And it's not just about the geometry of things we can see and touch. Geometry is also present in art, music, nature, physics, engineering, architecture, design, computer graphics, and many other areas of knowledge. Therefore, understanding the geometry of regular polygons is a fundamental skill for many careers and daily activities.

Practical Activity: Polygons in the Construction of the Geometric City

Project Objective

This project aims to deepen the understanding of regular polygons and their properties, applying these concepts in the creation of a geometric city. The activity will also involve the discipline of Arts, as students will have to materialize their ideas in a three-dimensional model.

Detailed Project Description

Students will be divided into groups of 3 to 5 people, and each group will be responsible for creating a geometric city using regular polygons. In this city, each type of building (house, school, building, etc.) will be represented by a type of regular polygon. The city's streets and parks can also be arranged in regular polygon shapes.

During the creation of the city, students must:

1. Identify each regular polygon used in the project, informing the number of sides, and calculate the number of diagonals passing through the center.
2. Calculate the internal and external angles of each polygon used.
3. Solve problems involving the polygons used. For example, calculate the area of each polygon and deduce the amount of paint needed to paint the buildings.

In addition, students will need to prepare a detailed project report, where they must explain its relevance, describe the construction of the city, justify the choice of polygons, show the calculations performed, and discuss the results obtained.

Required Materials

For the project, students will need cardboard, ruler, pencil, colored pens, glue, scissors, and other materials they find necessary for the construction of the city's three-dimensional model.

Detailed Step-by-Step

1. Students should first research and review the concept and properties of regular polygons.
2. Next, they should choose which polygons will represent each building in the city.
3. Now is the time to create the city project. They must decide where each building will be positioned and which paths will connect these buildings.
4. After the planning phase, students should start building the three-dimensional model of the city.
5. While building the city, students must perform the necessary calculations involving the polygons used.
6. Finally, students must prepare the final project report.

Project Delivery

The project will be considered completed when the three-dimensional city is ready, and the final report is presented. The report must follow the following structure:

1. Introduction: Students must contextualize the theme, explain its relevance, and the project's objective.
2. Development: Students must describe the city's construction process, justify the choice of polygons, and detail the calculations performed.
3. Conclusions: Students must present the results obtained, the difficulties encountered, what they learned in the process, and their final conclusions.
4. Bibliography: Students must list all sources of information used for the project.

Remember that the purpose of this project is not only to learn about regular polygons but also to develop skills such as teamwork, time management, problem-solving, and creativity.