Contextualization

Mathematics is a universal language, being essential for us to understand and interact with the world. In the first year of high school, we studied various forms and concepts, including the trapezium. Such a geometric figure, which is characterized as a quadrilateral with only one pair of parallel sides, is a theme of wide practical application, being found in several areas of knowledge, such as Architecture, Engineering, Drawing and Art.

Understanding the concept of a trapezium, its properties and how to calculate its area and perimeter are fundamental skills in the high school mathematics curriculum. These competencies are essential not only for progress in the study of geometry, but also for application in other disciplines and practical situations.

In our daily lives, trapezoids can be found in a variety of places, from a skateboarder's board to the wing of an airplane. In addition, in architecture, the trapezium can be used to create structures and buildings with an interesting and dynamic design.

Theoretical Introduction

The trapezium is a quadrilateral (a polygon with four sides) where only one pair of opposite sides is parallel. These parallel sides are called the base and the non-parallel sides are called the non-parallel or lateral sides. The distance between the bases is called the height.

There are different types of trapezoids. The isosceles trapezoid, where the non-parallel sides are equal and the angles adjacent to the same base are equal. The rectangular trapezium, which has a right angle between the parallel and non-parallel sides, and the scalene trapezium, where all sides and angles are different.

The area of a trapezoid is calculated using the formula: A = (B+b).h/2, where A is the area, B and b are the lengths of the bases and h is the height. So, to calculate the area of a trapezoid, we need to know the lengths of the bases and the height.

Practical Activity: "Building the World with Trapezoids"

Project Objective

The project "Building the World with Trapezoids" aims at the practical application of the theoretical concepts related to trapezoids. Students should, in groups of 3 to 5 people, elaborate and execute a project that uses trapezoids in its design. The project may involve creating a physical model or a detailed drawing.

Detailed Description of the Project

Students will have to research, plan and execute a project that has trapezoids as a fundamental design element. The project can be the plan of a building, the drawing of a bridge, the creation of a decoration object, an artistic drawing or even a plan of a city.

In addition, students will need to understand and apply trapezoid concepts to calculate areas, perimeters and angles, using this data to assist in the planning and execution of their project.

Required Materials

• Pencils and paper for planning
• Drawing material (colored pencils, pens, etc.) for creating the final project
• Ruler and protractor for accurate measurements and angles
• (Optional) Model building materials (cardboard, glue, scissors, etc.)

Detailed Step-by-Step

1. Form groups of 3 to 5 students.
2. Research and discuss project ideas.
3. Choose a project to execute and make a detailed plan.
4. Draw or build the project, ensuring that the trapezoids are present and well represented.
5. Calculate and record all the relevant measures (heights, bases, areas, perimeters, angles) of the trapezoids used.
6. Reflect on the process and results obtained, preparing a detailed report.

Project Deliveries and Paper Writing

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

1. The final project (drawing or model).
2. A Project Report, which must contain:

Introduction:

Here, the students should discuss the general idea of the project, the relevance of the trapezoids and how they were applied in their project. The introduction should also contain the group's objectives for the project.

Development:

In this section, students should discuss the theory of trapezoids, detailing how the theoretical concepts were used in practice during the execution of the project. This should include a detailed discussion of the measurements and calculations performed, in addition to a step-by-step description of how the project was executed.

Conclusions:

Students should review the objectives mentioned in the introduction and discuss whether or not they were achieved, explaining the reasons. Here, one should also reflect on what learned during the project, not only about trapezoids, but also about teamwork and project planning.