Contextualization

Geometry is part of the world we live in, and understanding its fundamental concepts offers a unique insight into how things work. In this project, we will explore one of these fundamental concepts - the area of the triangle.

The triangle is one of the most basic geometric figures. It has three sides and three angles. The area of the triangle, which is the measure of the space within the triangle's boundaries, is a very important concept in geometry. To calculate the area of a triangle, we need to know the length of the base (any of the sides) and the height (the perpendicular distance from the opposite vertex to the base). The formula to find the area is given by 1/2 base * height.

The area of the triangle is used in various domains of everyday and professional life, including engineering, art, architecture, agriculture, and more. For example, architects and engineers use the concept of the triangle area to calculate the space needed for specific projects. Similarly, in agriculture, farmers use this concept to determine the area of their lands for planting or grazing purposes.

Understanding the area of the triangle is also a cornerstone for understanding more complex mathematical concepts, such as trigonometry. Therefore, by mastering this topic, you will be building a solid foundation for mastering many other advanced mathematical concepts.

Practical Activity: "Triangle Area: Construction, Measurement, Calculation, and Application"

Project Objective

The objective of this activity is for students to understand and apply the theory of calculating the area of the triangle. The project also aims to encourage teamwork, improve communication skills, and stimulate creativity and problem-solving.

Detailed Project Description

The group of students will carry out a series of activities involving the concept of the triangle area, namely:

1. Construction and drawing of a triangle: students should draw and build a large triangle on cardboard or cardstock, with the sides and height clearly measured and noted.
2. Area calculation: students should use the triangle area formula to calculate the area of the triangle they built.
3. Creation of a three-dimensional object (pyramid): the group will build a pyramid with a triangular base using the triangle they previously built.
4. Calculation of the pyramid's volume: students should learn and apply the formula for the volume of the triangular pyramid to calculate the volume of the pyramid they built.
5. Application of the concept: the group will identify and analyze a real-world problem involving the calculation of the triangle area, proposing solutions using the concepts learned.

Required Materials

• Cardboard or cardstock
• Ruler
• Markers or pens
• Tape measure
• Glue and scissors

Step by Step

1. On the cardboard, draw a large triangle, using a ruler to measure the sides and marking the height.
2. Using the triangle area formula, calculate the area of the triangle you drew. Record this information.
3. Build a pyramid with a triangular base using the triangle you drew. The height of the pyramid can be determined by the group.
4. Using the pyramid's volume formula, calculate the volume of the pyramid you built. Record this information.
5. Identify a real-world problem involving the calculation of the triangle area and propose solutions. For example, if your school wanted to build a new triangular wing, what would be the best design to maximize space?

Project Deliverables

Students should deliver both the physical triangle and pyramid they built, as well as a detailed written report of the project. The report should contain the following elements:

1. Introduction: In this section, the group should introduce the concept of the triangle area, explain its importance in real-world situations, and define the project's objective.
2. Development: Here, the group should explain, step by step, the process of drawing and building the triangle and pyramid, how they calculated their area and volume, and how they applied the concept of the triangle area to a real-world problem. The group should also discuss the results obtained, comparing them to the initial expectations.
3. Conclusion: In this part, the group should comment on what they learned from the experience, what difficulties were encountered and overcome, and what lessons can be drawn from the project.
4. Bibliography: The group should list all sources of information used to carry out the project, both for the theoretical part (learning about the triangle area and the pyramid volume formula) and for the practical part (construction of the triangle and pyramid).

This project has an estimated duration of 12 to 15 hours per student and should be carried out by a group of 3 to 5 students.