Contextualization

Area is a fundamental concept in geometry and one of the main topics studied in the 7th grade. It is basically the amount of space an object occupies on a surface. Therefore, it is an essential concept for understanding spaces in different contexts, from calculating spaces for painting to civil construction and agriculture. In this project, we will focus on studying a specific type of geometric figure, the Trapezoid.

Trapezoids are quadrilaterals that have two parallel bases of different lengths, while the other two sides, which are not parallel, are called lateral sides. The height of the trapezoid is the perpendicular distance between the bases. Trapezoids are very common in various everyday situations, although sometimes we do not recognize them immediately. For example, a boat sail is a trapezoid, as well as the shape of many bridges and buildings.

Trapezoids are vital in design and engineering, for example, as they offer a combination of strength and stability that is hard to achieve with other geometric shapes. The area of a trapezoid is calculated by the formula:

A = (B + b) / 2 * h, where 'A' is the area, 'B' is the larger base, 'b' is the smaller base, and 'h' is the height.

Practical Activity

Activity Title: Building and Measuring Trapezoids

Project Objective

The fundamental objective of the project is to provide students with a practical understanding of the concept of area and how it applies to geometric figures like the Trapezoid, as well as to provide them with a meaningful experience of teamwork collaboration.

Detailed Project Description

In this activity, groups of students will build trapezoids using simple materials and then calculate their areas based on actual measurements. The task will require prior knowledge about trapezoids, measurements in cm and m², and the formula to calculate the area of a trapezoid.

Required Materials

• Cardboard paper of different colors
• Rulers
• Pencils
• Scissors
• Calculators
• Notebook to record calculations and observations

Detailed Activity Steps

1. Divide the class into groups of 3 to 5 students.
2. Each group will receive a sheet of cardboard paper, a ruler, a pencil, and scissors.
3. Each group should draw an arbitrary-sized trapezoid on the cardboard paper and cut it out.
4. With the help of the ruler, students should measure the larger base, the smaller base, and the height of the trapezoid.
5. Using the trapezoid area formula, students will calculate the area of the trapezoid in square centimeters.
6. All calculations and measurements should be recorded in a notebook.
7. After completing the practical activity, each group should prepare a detailed report of their experience, from the construction process to the area calculation.

Project Deliverables

Students must produce two main outcomes:

1. Cardboard Paper Trapezoid: Each group must present the cardboard paper trapezoid they built with the measurements and area calculations clearly annotated.

2. Project Report: Groups should write a report documenting their process and results. The document should include:

   • Introduction: In this section, students will describe the purpose of the project, give a brief explanation of the trapezoid area theory, and explain why it is an important concept in mathematics and everyday applications.

   • Development: Here students will explain in detail the work they carried out. They should start with the theory used for the activity execution, followed by a detailed description of the trapezoid construction, the process of measuring its characteristics, and calculating its area. They should also explain the challenges encountered and how they solved them.

   • Conclusion: This section should include a summary of what was learned from the project, both in terms of mathematical knowledge and teamwork skills. Students should reflect on how their understanding of area and the trapezoid changed as a result of the project.

   • Bibliography: Students should list any resources (books, websites, videos) they used to help complete the project.

Students will have one week to complete the activity and deliver the Cardboard Paper Trapezoid and the Project Report.