Contextualization

Mathematics is a science that accompanies us in all spheres of life, and geometric shapes are present in many contexts of our daily lives. In this project, we will focus on the figure of the trapezoid, which is a special form of quadrilateral.

Trapezoids are geometric figures that have four sides, but only two of them are parallel to each other. These parallel sides are called bases, and the non-parallel sides are called lateral sides. The shortest distance between the bases is the height of the trapezoid. With these three pieces of information: bases and height, we can calculate the area of a trapezoid.

Now, you might be wondering, why should we learn to calculate the area of a trapezoid? Well, because the trapezoid is a very common figure in our lives. Look around you, and you will find trapezoids in many places: on a slice of pizza or pie, on the wing of an airplane, in the form of terraces or farms, on mountain slopes, in certain types of pools, and even in the design of certain products we use in our daily lives. Therefore, knowing and being able to calculate the area of a trapezoid is relevant not only for Mathematics but also for real life.

There are several interesting applications and problems that can be solved with the help of trapezoid area calculation. For example, in Physics, the trapezoid area is used to calculate the distance traveled by an object in motion over a certain period of time. In Engineering and Architecture, calculating the trapezoid area is useful for designing roofs, ramps, aqueducts, and many other structures.

To start exploring these concepts and applications, we recommend some resources that may be useful:

• OBMEP Mathematics Portal: Trapezoid
• Khan Academy: Trapezoid Area

By the end of this project, you will be able to calculate the area of any trapezoid and will have a deeper understanding of the applications of this calculation in the real world. Let's go!

Practical Activity

Activity Title: "Keeping an Eye on the Trapezoid"

Activity Objective:

This project aims to practice and improve the calculation of trapezoid areas. It also aims to enhance students' ability to work in teams, solve problems, think critically, and manage time.

Detailed Project Description:

Students will be divided into groups of 3 to 5 people. Each group will be challenged to find at least five trapezoids in their surroundings (school, home, city, etc.) and measure their dimensions for the calculation of their areas. Subsequently, they must create a detailed report of this experience, including the theory behind the calculation of a trapezoid's area and the results obtained.

Required Materials:

1. Ruler or measuring tape
2. Camera (can be a cellphone camera)
3. Notebook and pen for notes
4. Internet access for research

Detailed Step-by-Step:

1. Group Formation: Students must organize themselves into groups of 3 to 5 people, which will be maintained throughout the project.

2. Research and Study: Groups must research and study about the trapezoid and how to calculate its area.

3. Search for Trapezoids: Each group must find at least five trapezoids in their surroundings and take photos of them.

4. Measurement: After identifying the trapezoids, students must measure the bases and height of each trapezoid found.

5. Calculation: Using the formula for calculating the trapezoid area, students must calculate the area of each identified trapezoid.

6. Discussion and Analysis: Each group must discuss and analyze the results obtained, seeking to understand the differences between the identified trapezoids and their areas.

7. Report Writing: Finally, groups must write a detailed report, explaining the theory behind the calculation of a trapezoid's area, the methodology used to find and measure the trapezoids, the results obtained, and the discussion around these results.

Project Deliverables:

The final project should consist of a detailed written report, which should include the following topics:

1. Introduction: Explain the project's objective, the relevance of calculating the trapezoid area, and its real-world application.

2. Development: Detail the theory behind the calculation of a trapezoid's area, the methodology used to find and measure the trapezoids, and the results obtained. The photos taken of the found trapezoids should be included in this topic, always with an explanation of where the trapezoid was found and its measurements.

3. Conclusion: Discuss the results obtained, what you learned from this project, and your main conclusions.

4. Bibliography: List the resources you used to conduct research and complete the project.

It is important to note that report writing should be considered a crucial component of the project and should be done collaboratively among group members. The report is not only a means of communicating the project's results but also a tool for learning to organize ideas, improve writing, and argumentation skills.