Context

Mathematics is an incredibly diverse and comprehensive field that goes far beyond numbers. It is not only an academic discipline but also a science that extends across numerous practical and theoretical fields. We learn mathematical concepts throughout our lives and apply them in different contexts. One of these concepts is the calculation of area, especially concerning composite figures, which are figures formed by the union of two or more basic shapes (such as triangles, squares, and rectangles).

Calculating the area of composite figures is an essential skill in various professions and daily activities, from architecture and engineering to agriculture and interior decoration. For example, when designing a house, it is necessary to calculate the area of the land to determine how the space will be used. Similarly, when painting a room, it is necessary to add up the area of the walls to estimate the amount of paint needed.

Introduction

The study of geometry is a fundamental branch of mathematics that involves the study of the properties and relationships of figures in the plane. In this project, we will specifically explore the concept of areas of plane figures, focusing on composite figures. Composite figures are formed by the combination of two or more simple shapes, such as a rectangle and a triangle to form a box-shaped house.

The area calculation is done by measuring the amount of surface occupied by the figure, based on the established unit of measurement. In the case of composite figures, the areas are calculated separately and then added together to obtain the total area. Knowledge of these techniques is essential for solving geometry problems and has applications in various fields of knowledge.

By the end of this project, you will be able to calculate the area of composite figures by breaking them down into simpler shapes. We hope this experience will offer you a new perspective on an important part of mathematics and foster valuable skills such as teamwork, time management, and creative thinking.

Practical Activity

'Drawing and Calculating the Area of Composite Figures'

Project Objective:

The objective of this project is to allow students to apply the concepts of calculating the area of composite figures in a practical and fun scenario, developing their teamwork, time management, and creative thinking skills.

Detailed Project Description:

Each group of 3 to 5 students must create a map of an imaginary amusement park. This map should be drawn with care and creativity, featuring at least 5 different types of attractions (roller coaster, Ferris wheel, haunted house, etc). Each attraction will be represented by a composite figure, which can be formed by any basic shapes (squares, rectangles, triangles, etc).

After drawing the map, students must calculate the area of each attraction (composite figure) in the park. Additionally, they should also calculate the total area occupied by the attractions, that is, the sum of the areas of all the composite figures drawn.

Materials Needed:

• Drawing paper or large-sized cardboard.
• Markers, colored pencils, or paints for coloring.
• Ruler and compass to assist in drawing the figures.
• Calculator to expedite calculations.

Detailed Step-by-Step Guide for the Activity:

1. Formation of groups of 3 to 5 students.
2. Discussion and planning of the design of the park map and its attractions.
3. Drawing of the composite figures representing each park attraction on the drawing paper.
4. Measurement of the basic shapes that make up each composite figure.
5. Calculation of the area of each basic shape and then of the composite figures.
6. Summation of the areas of all composite figures and conclusion of the total park area.
7. Coloring and finishing the drawing.
8. Writing the report detailing the experience and presenting the calculated results.

Project Deliverables and its relation to the activity:

Students must submit the drawn map, accompanied by a report explaining the entire process of creating the amusement park and calculating the areas. The report should be divided into the following sections:

• Introduction: The student must contextualize the theme, discussing the importance of calculating the areas of composite figures in real life, the relationship with the project, and its objective.

• Development: Students must explain the theory behind area calculations, detail the activity performed, including the drawing of the figures and the methodology used to calculate the areas. They should also present and discuss the results obtained, inserting the measurements and calculations made.

• Conclusion: Students must summarize the main points of the work, reflecting on what they have learned and the conclusions drawn from the project. They should also discuss the socio-emotional skills developed during the project.

• Bibliography: Students must indicate the sources used for the project development, such as books, web pages, videos, etc., cited in the Resources section of the Introduction.

This written report will be an opportunity to express the learnings from the project, relating the practical part (drawing creation and area calculations) to the theory studied. Additionally, the report will also be a source of reflection on teamwork and the skills developed.