Contextualization

Geometry is one of the oldest branches of mathematics, having been used throughout history to solve problems related to land measurement, building construction, and navigation. In this project, we will focus on a fundamental component of geometry: the triangle. This simple polygon with three sides can be found in architectural structures, art, nature, and even in more advanced mathematical concepts such as trigonometry and vector calculus.

Studying the area of a triangle is a first step towards understanding more complex concepts. Although it is a simple concept, the area of a triangle plays a crucial role in many fields of science and engineering. In civil engineering, it is used to design stable structures. In agronomy, it helps determine the amount of resources needed to maintain a plantation. Even in aviation, it is used to calculate the lift of an airplane's wings.

Introduction

Triangles are a geometric figure that can be simply defined as a figure with three sides. However, triangles have some interesting properties that distinguish them from other shapes. For example, the sum of their interior angles is always 180 degrees, and they are the only shape that will always be rigid, meaning it cannot be deformed without changing the length of the sides.

The area of a triangle is calculated as half of the product of the base by the height length. This is the most common formula, but there are other ways to find the area of a triangle when certain information is known, such as Heron's formula to find the area when the lengths of the three sides are known.

Finally, it is important to note that although the area of a triangle is a relatively simple concept, it forms the basis for calculating the area of other more complex shapes. In fact, any polygon can be divided into triangles, and the area of a polygon is then equal to the sum of the areas of its constituent triangles.

Practical Activity

"Geometry in Action: Measuring Our School"

Project Objectives:

This project aims to provide students with a practical understanding of the importance of calculating the area of a triangle, being an effective way to illustrate the application of theory to practice. Students will calculate the area of different parts of the school using the triangle area formula and measurement applications.

Detailed Project Description:

Students will be divided into groups of 3 to 5 people. Each group will receive a specific area of the school to measure. This area can be a soccer field, a garden, the parking lot, among others.

Students must first gather the necessary tools and outline an action plan for measuring the area. After collecting data, they will use the measurements obtained to calculate the area of the designated space, using the triangle area formula. Students are also encouraged to explore different ways of triangulation for their measurements.

After the measurements and calculations, the groups must prepare a report describing the process, the difficulties encountered, the solutions found, and the final project outcome.

Necessary Materials:

1. Tape measure or measuring tapes (preferably one that measures up to 50 meters).
2. Notebook or sheets of paper for notes.
3. Pen or pencil.
4. Calculator.
5. Digital camera or cell phone (to document the process).

Detailed Step-by-Step:

1. Planning: Draw a sketch of the area to be measured and plan the best way to divide the area into triangles for measurement. This plan should be included in the final report.

2. Measurement: Use the tape measure to measure the sides of the planned triangles. Record all measurements.

3. Calculation: Use the measurements obtained to calculate the area of each sector of the total area using the triangle area formula.

4. Report Preparation: Write a detailed report of the project including the points required below.

Project Delivery:

Students must submit a written report addressing the following topics:

1. Introduction: Provide context for the theme, its relevance and real-world application, as well as the objective of this project.

2. Development: Explain the theory behind the calculation of the area of a triangle, describe the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.

3. Conclusion: Summarize the main points, explaining the learnings obtained and the conclusions drawn from the project.

4. Bibliography: Indicate the sources they relied on to work on the project such as books, web pages, videos, among others.

This report must be submitted both in digital and printed format to the teacher. The deadline for submitting the report is one month from the start date of the project.