Context

The area of objects and its measurement are fundamental aspects of mathematics, influencing various disciplines such as geometry, engineering, architecture, agronomy, etc. Learning how to calculate the area of simple geometric shapes, such as rectangles and parallelograms, is the first step to understanding how to calculate the area of more complex shapes.

A rectangle is defined as a quadrilateral with all internal angles equal (90º). It is formed by two pairs of parallel sides, and the opposite sides are equal. The formula for the area of a rectangle is simply the length times the width (A = l * w).

A parallelogram is a quadrilateral whose opposite sides are parallel. In a parallelogram, the opposite sides are equal, and the opposite angles are also equal. The area of a parallelogram is given by the product of its base and height (A = b * h).

It is very important for you to understand these geometric shapes and how to calculate their areas because this understanding will be vital in many topics and future disciplines you will study, including other areas of mathematics, physics, engineering, etc.

The ability to calculate the area of rectangles and parallelograms has a variety of practical applications in different professional fields. For example, when designing a building's floor plan, architects use the area to determine the amount of material needed. In agriculture, the area is used to determine the amount of fertilizer or seed needed for a field.

Practical Activity

Activity Title: Building and Calculating Areas with Rectangles and Parallelograms

Project Objective:

Build rectangles and parallelograms using concrete materials, calculate their areas, and prepare a report exposing the concepts learned, the methodology used, and the results obtained.

Detailed Project Description:

The groups will create rectangles and parallelograms using popsicle sticks. They will calculate the area of these shapes using the corresponding formula. In the end, they will prepare a detailed report explaining the theoretical concept, the methodology used, and reporting the results obtained.

Required Materials:

1. Popsicle sticks
2. Tape measure or ruler
3. Paper and Pencil
4. Calculator

Detailed Step-by-Step for the Activity:

1. Group Formation and Material Distribution: Form groups of 3 to 5 students. Each group should receive popsicle sticks, a tape measure or ruler, paper and pencil, and a calculator.
2. Construction of Figures and Measurement: The groups will build various shapes of rectangles and parallelograms using popsicle sticks. They will measure the base and height of each shape using the tape measure or ruler.
3. Calculation of Areas: After measuring the base and height, the students will calculate the area of each shape using the formulas for the area of a rectangle (A = l * w) and parallelogram (A = b * h).
4. Report Preparation: Each group will prepare a report detailing the theoretical concepts, the methodology used, and the results obtained. The report should include introduction, development, conclusions, and bibliography.

Project Deliverables:

1. Physical Shapes: The shapes of rectangles and parallelograms made with popsicle sticks.
2. Report: The written report detailing the entire project process, with the following points:
   1. Introduction: Contextualizing the theme, its relevance and application in the real world, in addition to the objective of this project.
   2. Development: Exposing the theory behind the central theme of the project (calculation of areas of rectangles and parallelograms), explaining the activity in detail, indicating the methodology used (construction of shapes, measurement, and area calculation) and discussing the results obtained.
   3. Conclusion: Summarizing the main points, explaining the learnings obtained, and drawing conclusions about the project.
   4. Bibliography: Indicating the sources they relied on to work on the project (books, web pages, videos, etc.)

Students must present the learned concepts in a coherent and structured manner, using the collected data. They must demonstrate a clear understanding of the area calculation process and the practical application of this skill.