Lesson Plan | Lesson Plan Tradisional | Spatial Geometry: Surface Area of the Prism

Objectives

Duration: (10 - 15 minutes)

The aim of this phase is to give learners a solid understanding of the lesson objectives, priming them for the topics at hand and establishing clear expectations of what they should be able to achieve by the lesson's end.

Objectives Utama:

1. Clarify the concepts of lateral surface area and total surface area of a prism.

2. Introduce the formula for calculating both the lateral surface area and total surface area of a prism.

3. Apply these concepts to solve real-world problems.

Introduction

Duration: (10 - 15 minutes)

📊 Purpose: This stage aims to create an initial context that sparks students' interest in the lesson topic. By linking the material to practical applications and intriguing facts, students will be more engaged and motivated to learn about the surface area of prisms.

Did you know?

🔍 Curiosity: Did you know architects and engineers rely on concepts of surface area to figure out the amount of materials needed for building structures? For example, when planning a new building, they need to know the area of the outer walls to estimate how much paint or coating is required. Additionally, in packaging design, understanding surface area helps decide how much material goes into making product boxes.

Contextualization

📐 Context: To kick off the lesson, explain to the class that Spatial Geometry is a key branch of Mathematics that focuses on three-dimensional shapes. One of the most familiar solids is the prism, which appears in various forms in our everyday lives — think buildings, boxes, and even some furniture. Gaining insight into the properties of prisms, particularly their surface area, is crucial for many practical applications, from construction to packaging design.

Concepts

Duration: (45 - 55 minutes)

📊 Purpose: This stage is designed to enhance students' understanding of the surface area of prisms, providing a strong theoretical and practical foundation through detailed examples and questions to be worked out. This will enable students to apply these concepts in different contexts, equipping them to tackle real-world and academic challenges confidently.

Relevant Topics

1. 📐 Definition of Prism: Clarify that a prism is a geometric solid with two parallel and congruent bases, and lateral faces that are parallelograms. The bases can take on any polygonal shape, like triangles, squares, or hexagons.

2. 📏 Lateral Surface Area Formula: Indicate that the lateral surface area of a prism is the total of the areas of all its lateral faces. To compute this, multiply the perimeter of the base by the height of the prism. Formula: A_l = p * h, wherein p signifies the perimeter of the base and h is the height of the prism.

3. 📏 Total Surface Area Formula: Explain that the total surface area of a prism equals the lateral surface area plus the areas of the two bases. Formula: A_t = A_l + 2 * A_b, where A_l is the lateral area and A_b is the area of the base.

4. 📊 Practical Examples: Present relatable examples, such as calculating the area of a prism with a triangular base and a rectangular prism. Demonstrate the step-by-step calculations, from determining the perimeter of the base to summing the areas of the bases and lateral faces.

5. 🏗️ Everyday Applications: Discuss how these calculations are used in everyday situations, like in construction to figure out material quantities, or in packaging design to calculate how much cardboard or plastic is needed for boxes.

To Reinforce Learning

1. Calculate the lateral surface area and the total surface area of a rectangular prism with a base of 4 cm by 6 cm and a height of 10 cm.

2. A triangular prism has bases with sides of 3 cm, 4 cm, and 5 cm and a height of 12 cm. Determine the lateral surface area and the total surface area of this prism.

3. A room is shaped like a rectangular prism, measuring 5 m in width, 8 m in length, and 3 m in height. Calculate the total area of the walls that need to be painted.

Feedback

Duration: (20 - 25 minutes)

📊 Purpose: This phase is meant to ensure students solidify the knowledge acquired during the lesson, clearing up any lingering doubts and reinforcing concepts through collective discussion and reflection. This space allows you to gauge students' understanding and adjust your teaching as necessary.

Diskusi Concepts

1. 📐 Discussion of the Questions: 2. Question 1: To calculate the lateral surface area of a rectangular prism with a base of 4 cm by 6 cm and a height of 10 cm, follow these steps: 3. Perimeter of the Base: p = 2 * (4 cm + 6 cm) = 20 cm 4. Lateral Surface Area: A_l = p * h = 20 cm * 10 cm = 200 cm² 5. Area of Each Base: A_b = 4 cm * 6 cm = 24 cm² 6. Total Surface Area: A_t = A_l + 2 * A_b = 200 cm² + 2 * 24 cm² = 248 cm² 7. Question 2: To calculate the lateral surface area of a triangular prism with sides of 3 cm, 4 cm, and 5 cm and a height of 12 cm: 8. Perimeter of the Base: p = 3 cm + 4 cm + 5 cm = 12 cm 9. Lateral Surface Area: A_l = p * h = 12 cm * 12 cm = 144 cm² 10. Area of the Base (using Heron's formula): A_b = √(s * (s - a) * (s - b) * (s - c)), where s = p / 2 = 6 cm, a = 3 cm, b = 4 cm, c = 5 cm 11. A_b = √(6 * (6 - 3) * (6 - 4) * (6 - 5)) = √(6 * 3 * 2 * 1) = √36 = 6 cm² 12. Total Surface Area: A_t = A_l + 2 * A_b = 144 cm² + 2 * 6 cm² = 156 cm² 13. Question 3: To calculate the total area of the walls of a room shaped as a rectangular prism with dimensions of 5 m width, 8 m length, and 3 m height: 14. Area of Each Wall: 15. Wall 1: 5 m * 3 m = 15 m² 16. Wall 2: 8 m * 3 m = 24 m² 17. Total Area of the Walls: 2 * (15 m² + 24 m²) = 2 * 39 m² = 78 m²

Engaging Students

1. 🔍 Student Engagement: 2. Encourage students to share any challenges they faced using the formulas for perimeter and area. Discuss these challenges and how to tackle them. 3. Invite students to phrase in their own terms how to calculate the lateral surface area and total surface area of a prism. Foster participation from all. 4. Encourage students to think of other practical situations where they could apply what they've learned, beyond the examples given. 5. Offer an additional exercise: Calculate the area of a hexagonal prism with a perimeter of 30 cm and a height of 10 cm. Discuss potential strategies to solve this problem.

Conclusion

Duration: (10 - 15 minutes)

The aim in this phase is to recap and solidify the key points covered throughout the lesson, reinforcing students' understanding and underscoring the practical significance of the content. This reflection period helps fortify learning and contextualize the relevance of the topic in students' daily lives.

Summary

['Definition of a prism as a geometric solid featuring two parallel and congruent bases with lateral faces that are parallelograms.', 'Formula for calculating the lateral surface area of a prism: A_l = p * h.', 'Formula for calculating the total surface area of a prism: A_t = A_l + 2 * A_b.', 'Practical examples showcasing the calculations for lateral and total surface area of prisms with varying bases.', 'Real-world applications of surface area calculations across fields like construction and packaging design.']

Connection

The lesson effectively bridged the theoretical aspects of calculating lateral and total surface areas of prisms with practice by presenting detailed examples and questions that relate these concepts to real-life problems, such as estimating the paint required for room walls or the materials used in product packaging.

Theme Relevance

Grasping how to compute the surface area of prisms is vital in everyday life, as this knowledge finds application in various practical scenarios. For instance, architects and engineers use these concepts to ascertain the volume of construction materials needed for projects, and in packaging design, these calculations help maximize the efficient use of materials like cardboard and plastic.