Contextualization

The concept of area is a fundamental aspect of mathematics that we use every day, whether consciously or unconsciously. From calculating the amount of carpet needed to cover a room to determining the space required for a garden, understanding the area helps us to make practical decisions in our daily lives.

Area is the size of a two-dimensional surface. It can be thought of as the amount of space inside a shape. Simple shapes, such as rectangles and triangles, have formulas that can be used to quickly find their areas. However, when it comes to more complex shapes, like a room with an alcove or a garden with a pond, we need to use the concept of Composite Figures.

A composite figure is a figure made up of two or more simple shapes. By splitting the composite figure into these simple shapes and calculating their individual areas, we can then sum these areas together to find the total area of the composite figure.

The concept of composite figures is not only a key component of geometry, but it is also an essential skill for problem-solving. In real-world scenarios, we often encounter shapes that are not simple and require us to break them down into more manageable parts. By understanding how to find the area of a composite figure, we can solve these problems effectively and efficiently.

The area of composite figures is a bridge between geometry and arithmetic. While the formulas for finding the area of a rectangle or triangle are based on geometric principles, calculating the area of a composite figure involves addition and multiplication, fundamental concepts in arithmetic.

In this project, we will not only delve into the theory behind the area of composite figures but also explore its practical applications in real-world scenarios. We will discover how this concept is utilized in various industries, from architecture to landscaping, and how it helps us in our everyday decision-making.

Here are some resources to help you understand the concept of area of composite figures in more depth:

1. Khan Academy: Area of Composite Shapes
2. Math is Fun: Area of Composite Shapes
3. Study.com: Finding the Area of a Composite Shape
4. Book: "Mathematics in Our World" by David Sobecki, Brian Mercer, and Allan G. Bluman.

Let's embark on this journey to explore the fascinating world of composite figures and its role in mathematics and real life!

Practical Activity

Title: Designing the Perfect Picnic Park

Objective of the Project

The objective of this project is to design a picnic park, an area that contains both simple and complex geometric figures, and calculate the area of this composite figure.

Detailed Description of the Project

In this project, each group will create a blueprint of a picnic park. The park must include at least one rectangle, one triangle, one circle, and one irregular shape (composed of two or more simple shapes). The students will then calculate the total area of the park, which is the sum of the areas of all these shapes.

The students will also conduct research on the practical applications of the area of composite figures in real life. They will present their findings in a written report, including the process they followed to design the park and calculate its area, and the implications of their findings in real-world scenarios.

Necessary Materials

• Graph paper
• Pencil and eraser
• Ruler and compass (for drawing accurate shapes)
• Calculator
• Internet access for research

Detailed Step-by-Step for Carrying Out the Activity

1. Brainstorm and Plan: As a group, discuss and decide on the design of your picnic park. Remember, it must include at least one rectangle, one triangle, one circle, and one irregular shape. Sketch the design on a rough paper.

2. Draw the Shapes: On the graph paper, using the ruler and compass (where necessary), draw the shapes according to your design. Make sure to label each shape with its dimensions.

3. Calculate the Areas: For each shape, calculate its area using the appropriate formula (rectangle: length x width, triangle: 1/2 x base x height, circle: π x radius^2). Write down the calculated areas beside each shape.

4. Divide and Conquer: If you have an irregular shape, break it down into simple shapes (rectangle, triangle, etc.). Calculate the area of each simple shape and write it beside the shape.

5. Total Area Calculation: Sum up all the areas to find the total area of your picnic park.

6. Research and Report Writing: Conduct research on the practical applications of the area of composite figures in real life. Write a detailed report of your project, following the structure provided (Introduction, Development, Conclusion, and Used Bibliography).

Project Deliverables

Each group should deliver:

1. A Picnic Park Blueprint: A neat and accurate blueprint of their picnic park, drawn on graph paper. This should include all the shapes used and their dimensions.

2. Area Calculations: The calculated areas of all the shapes used in the park, along with the total area.

3. A Written Report: The report should be structured as follows:

   • Introduction: Contextualize the theme, its relevance, and real-world application. State the objective of the project.

   • Development: Explain the theory behind the area of composite figures, detailing the steps taken in the project, the methodology used, and presenting the obtained results. Discuss the process of designing the park, calculating its area, and the implications of the findings in real-world scenarios.

   • Conclusion: Conclude by revisiting the main points, stating what was learned from the project, and drawing conclusions about the area of composite figures and its application.

   • Used Bibliography: Indicate the sources relied on to work on the project such as books, web pages, videos, etc.

Please note that the written report should not be a repetition of the steps taken but a detailed exploration of the project, the theory behind it, and the findings. The report should be written in a clear, concise, and engaging manner. Use visuals (such as diagrams, images, etc.) wherever possible to enhance understanding.

The total duration of the project should be around 12-15 hours per student, spread across one month. This includes the time spent on research, discussion, planning, designing, calculating, and writing the report. Remember, the goal is not just to complete the project, but to learn from the process!