Context

Mathematics is present in all aspects of our daily lives, and the concept of area is no exception. When painting a room, laying ceramic tiles on the floor, buying fabric for a curtain, or even planning the layout of furniture in a room, the use of areas is fundamental.

Area is the measurement of a surface and is expressed in square units. In our classes, we have already learned how to calculate the area of basic shapes such as squares, rectangles, and triangles. But what about when we come across more complex figures, which are composed of two or more of these basic shapes?

Theoretical Introduction

Composite figures are precisely this type of figure, formed by the combination of two or more simple figures (squares, rectangles, and triangles). To calculate the area of a composite figure, the strategy is to divide it into smaller parts, whose areas we already know how to calculate, and then add up these areas.

For example, imagine that we have a rectangle and a semicircle forming a composite figure, a pool for instance. To find the total area, we calculate the area of the rectangle and the semicircle separately and then add them together.

Importance and Real-World Applications

Calculating the areas of composite figures is a crucial skill not only for solving math problems but also has practical and real-world applications. Architects, engineers, interior decorators, landscapers, among others, often need to calculate the areas of composite figures in their work.

Furthermore, understanding this concept is also useful in everyday activities. For example, if you are planning to put grass in your irregularly shaped backyard, or if you want to paint a wall that has parts covered by windows and doors, you will need to calculate the area of composite figures.

Practical Activity

Activity Title: "Architecting Areas: Building Composite Figures"

Project Objective

This project aims to enhance students' ability to calculate the area of composite figures, working with theoretical concepts and applying them in a playful and collaborative way.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will be responsible for creating an architectural project of a fictional house on graph paper. The house must be composed of different rooms (rectangles, squares, and triangles), thus forming several composite figures.

Students must calculate the total area of their respective projects, as well as the area of each individual room. They must also propose practical solutions for the use of these areas in the house project, that is, allocate functions to each room according to its area.

Required Materials

• Graph paper
• Pencils and erasers
• Rulers
• Calculator (optional)

Detailed Step-by-Step

1. Divide the class into groups of 3 to 5 students.
2. Each group should draw on graph paper the floor plan of their fictional house, composed of different rooms (rectangles, squares, and triangles).
3. Students must calculate the area of each room and then the total area of the house.
4. Each group must also assign a function to each room according to its area (bedroom, kitchen, bathroom, living room, etc.).
5. The groups must present their projects to the class, sharing their calculations and justifications for the choices made in the room allocation.

Project Deliverables

In addition to the oral presentation, the groups must submit a written report containing:

1. Introduction: Description of the project, relevance of calculating the areas of composite figures, and the application of this concept in the real world.
2. Development: The theory behind area calculation, detailed house project including drawing, calculations performed, and the methodology used. The distribution of rooms and the justification for it should also be discussed.
3. Conclusion: Recap of the main points, discussion of what was learned, and conclusions about the work done.
4. Bibliography: References used to work on the project, including books, websites, videos, etc.

This document will serve as a written record of your project, complementing your oral presentation and the physical project of the house floor plan. It must be submitted after the project presentation.