Goals
1. Calculate the lateral and total surface area of a prism.
2. Apply these calculations to real-world scenarios, like figuring out the area of the walls in a room.
Contextualization
Spatial geometry is all around us, whether it’s in building construction or product packaging. Knowing how to calculate the surface area of prisms is vital for determining how much material is necessary for building or covering certain structures. Mastering these concepts can help tackle everyday challenges, like estimating how much paint is needed for a room or figuring out production costs for a box.
Subject Relevance
To Remember!
Definition of Prism
A prism is a three-dimensional shape with two identical, parallel bases, and lateral faces that are parallelograms. The base can be any polygon, and the height is the vertical distance between the bases.
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Prisms have two identical and parallel bases.
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The lateral faces of the prism are parallelograms.
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The height of the prism is the vertical distance between the bases.
Calculation of Lateral Surface Area
The lateral surface area of a prism is calculated by adding up the areas of all of its lateral faces. For rectangular prisms, you can find this by multiplying the perimeter of the base by the height of the prism.
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Lateral surface area only counts the lateral faces, not the bases.
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For rectangular prisms, multiply the perimeter of the base by the height.
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The general formula is: Lateral Area = Perimeter of the Base x Height.
Calculation of Total Surface Area
The total surface area of a prism is found by adding the lateral surface area to the areas of both bases. For rectangular prisms, this can be determined by taking the area of the bases and adding it to the lateral surface area.
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Total area includes both the lateral surface area and the two bases.
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For rectangular prisms, add the area of the bases to the lateral area.
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The general formula is: Total Area = Lateral Area + 2 x Base Area.
Practical Applications
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Civil Engineering: Calculate the amount of concrete needed to construct a prism-shaped column.
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Architecture: Work out how much paint is needed to cover the walls of a building.
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Interior Design: Estimate the amount of wallpaper required to decorate the entire room.
Key Terms
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Prism: A three-dimensional shape with two identical, parallel bases.
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Perimeter: The total length of all sides of a shape.
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Lateral Surface Area: The combined area of all the lateral faces of a prism.
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Total Surface Area: The combined area of the lateral surface area and the two bases of a prism.
Questions for Reflections
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How could knowing how to calculate the surface area of prisms benefit your career?
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What challenges might you encounter when applying these concepts in a real-world project?
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In what ways can understanding spatial geometry help you in other subjects or interests?
Practical Challenge: Calculating the Paint Needed to Paint a Room
Let’s put our knowledge to the test by solving a practical problem: calculating how much paint is necessary to cover all the walls of a rectangular prism-shaped room.
Instructions
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Imagine you have a rectangular room that measures 6 meters long, 4 meters wide, and 3 meters high.
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Calculate the lateral surface area of the room, with the walls representing the lateral faces of the prism.
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Determine the amount of paint required to cover all the walls, keeping in mind that 1 liter of paint covers 10 square meters.
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Present your calculations and explain the steps taken to achieve your result.
