Area: Rectangle and Parallelogram | Active Summary

Objectives

1.  Understand and apply the formula for the area of rectangles and parallelograms (A = base x height).

2.  Solve practical problems involving area calculations, such as determining the area of land for construction or agriculture.

3.  Develop critical thinking skills and practical application of mathematical concepts in the real world.

Contextualization

Did you know that calculating areas is not only crucial for architects and engineers, but also for agriculture and even for artists? For example, farmers use area calculations to optimize planting space, while artists can apply area concepts to create optical illusions in their works. This basic mathematical skill is a powerful tool that permeates many areas of our lives, helping to solve practical problems and foster creativity.

Important Topics

Area Formula for Rectangles and Parallelograms

The area formula for rectangles and parallelograms is essential to calculate the space occupied by these shapes. The area is calculated by multiplying the base by the height. In the case of parallelograms, the height is the perpendicular to the side that serves as the base.

• For rectangles, where all angles are 90 degrees, the height is any line that forms a 90-degree angle with the base.

• In the case of parallelograms, the height must be perpendicular to the base, but does not necessarily have to be one of the sides.

• Understanding and applying this formula is fundamental not only for academic mathematics, but also for practical applications such as interior design, architecture, and agriculture.

Calculating Areas in Practical Problems

Applying area calculations in real situations such as space planning, garden design, or land division is an example of the importance of mathematics in everyday life. These problems often involve combining various geometric shapes to optimize the use of available space.

• Solving these problems requires not only knowledge of the area formula but also logical and spatial reasoning skills.

• Practical examples include determining the amount of material needed to cover a floor or calculating the amount of soil required for a garden.

• The ability to apply area calculations in practical contexts is a valuable skill that transcends the school environment.

Professional and Daily Applications

Calculating areas is a fundamental skill for various professions such as architecture, engineering, agronomy, and design. Moreover, the ability to visualize and manipulate area concepts aids in understanding maps, building plans, and even art.

• Engineers use area calculations to plan roads and bridges, ensuring that land is used efficiently and safely.

• Architects rely on area calculations to create projects that meet the functional and aesthetic needs of spaces.

• In daily life, calculating areas can be useful for simple tasks such as planning furniture layout in a room or organizing a garden.

Key Terms

• Area: Measure of surface, expressed in square units, calculated by multiplying the relevant dimensions of a shape (length x width for rectangles and base x height for parallelograms).

• Rectangle: A quadrilateral with four right angles (90 degrees) and opposite sides equal. The area formula is simply base x height.

• Parallelogram: A quadrilateral with opposite sides parallel. The area formula is base x height, where the height is the distance between the parallel sides.

To Reflect

• How can calculating areas help solve organization problems in your home or school?

• In what way can understanding areas influence conscious consumption choices, such as buying materials for renovations or personal projects?

• What is the importance of learning mathematics applied to real-life situations and how can this benefit your life in the future?

Important Conclusions

• Today, we explored the fascinating world of areas of rectangles and parallelograms, learning to calculate the area of different shapes and apply this knowledge in practical situations such as interior design, agriculture, and architecture.

• We understood that mathematics is not just a theoretical discipline but an essential tool that permeates many aspects of our lives, helping to solve everyday and professional problems.

• The ability to calculate and apply areas not only enhances our mathematical skills but also develops our critical thinking and problem-solving capabilities, preparing us for future challenges.

To Exercise Knowledge

1. Draw Your House: Use the area formula to calculate and draw the layout of your house or a room. Think about how you would like to organize the furniture and calculate the necessary area for each item. 2. Garden Plan: Design a garden on graph paper using different geometric shapes. Calculate the total area of the garden and each type of plant you wish to include, considering the space each one needs to grow healthily. 3. Shopping Diary: Keep a diary for a week, recording every time you calculated areas, whether mentally or physically. This can include anything from the space occupied in the refrigerator to the size of a poster you wanted to buy.

Challenge

 Interior Designer Challenge: Imagine you are an interior designer and have a parallelogram-shaped space to renovate. Calculate the total area and divide the space into functional areas like a living room, kitchen, and bathroom. Create a visual project using an interior design app or simply drawing by hand to present your creative solution to the class in the next lesson!

Study Tips

•  Use Measurement Apps: Try augmented reality apps that allow you to measure real spaces using your phone's camera. This can help visualize how area formulas work in real objects and spaces.

•  Relate to Other Disciplines: Try to find connections between area calculations and other subjects, such as physics (to understand the distribution of forces in structures) or biology (to optimize plant growth in different environments).

•  Research Real Projects: Explore architecture and interior design projects online and try calculating the areas of different spaces. This can help see the practical application of the formulas and develop a deeper understanding.