Contextualization

The Prism is one of the most common geometric shapes in our daily lives. It can be found in objects, architectural structures, packaging, and even in clothing, thus becoming a fundamental figure for various branches of science such as Mathematics, Physics, and Engineering. The study of the prism's area is a crucial topic in mathematics, being a fundamental part to calculate its volume and better understand how this solid can change its shape without altering its volume.

This knowledge has several practical applications in our daily lives, especially in the fields of Civil Engineering, Architecture, and Design, where calculating the total area of a prism is important to determine the amount of material needed to cover a certain surface. Furthermore, this knowledge is also useful to better understand three-dimensional space, being applicable in practical situations such as organizing items in a box or creating models and three-dimensional mock-ups.

Theory

A prism is a three-dimensional geometric figure characterized by having two geometrically equal bases and lateral faces that are parallelograms. The bases can be regular or irregular polygons, creating prisms of various shapes and sizes.

The formula to calculate the area of a prism is given by the sum of the area of its bases with the area of its lateral faces. In the case of a regular prism, where all faces are equal, the calculation is simplified allowing to determine the total area with the application of simple formulas related to the elements of this polygon. However, for irregular prisms, the calculation can be quite complex and involves the use of advanced geometry concepts.

It is interesting to note that the study of plane tiling will be extremely useful in this project, as it will help in understanding the arrangement of the prism's faces and how they come together to form the solid.

Activity

Activity Title: Building and Exploring Prisms

Project Objective

This activity aims to familiarize students with the concept of prisms, their properties, and the application of these properties in solving practical problems. In addition, the project aims to encourage teamwork, effective communication, and the development of socio-emotional skills, such as time management.

Detailed Project Description

The groups, composed of 3 to 5 students, will build prisms using various materials such as cardboard, glue, and scissors. For each prism built, students must calculate the total area, considering the areas of its bases and lateral faces.

After construction and area calculation, students will investigate the effects of changing the dimensions of a prism on its total area, altering the height and shape of the bases for the same volume and comparing the results found.

Finally, students should locate examples of prisms in images or everyday objects and calculate their areas, applying the knowledge acquired in the practical activity.

Required Materials

• Cardboard of various colors
• Ruler
• Scissors
• Glue
• Pencil
• Calculator

Detailed Step-by-Step

1. The first step is to form the groups and explain the project in detail, clarifying any doubts that students may have.

2. Students should then study the theory of prisms, using the resources indicated in the introduction. They should seek to understand what a prism is, how to calculate its total area, and how this calculation relates to the shape of the bases and the height of the prism.

3. Next, each group should choose two types of prisms (for example, a triangular prism and a pentagonal base prism) and build them using cardboard, ruler, scissors, and glue.

4. After building the prisms, students should calculate the total area of each one, noting the calculations and the results obtained.

5. The next step is to change the height and shape of the prisms' bases without altering the volume, build the new prisms, and calculate the total area again.

6. After that, students should locate examples of prisms in images or everyday objects and calculate their areas, justifying their choices and explaining how they applied the concepts learned.

Project Deliverables

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

• The prisms they built;
• A detailed report containing the Introduction, Development, and Conclusions;
• Bibliographical references.

The report should include:

• Introduction: Here, students should contextualize the project topic, its real-life application, and the relevance of studying the total area of prisms. The project's objective should also be clearly stated.

• Development: This section should include the theoretical foundation of the project, a detailed description of the practical activity, the methodology used, and the presentation and discussion of the results obtained. Students should explain in detail the process of building the prisms, the total area calculations for each prism, and how these calculations relate to the theoretical concepts learned.

• Conclusions: In this segment, students should summarize the main points of the work, discuss what they learned from the project, and conclude on the applications of the concepts of a prism's total area in real-life contexts.

• Bibliography: Students should indicate the sources they used to elaborate the project, including books, websites, videos, among others.