Lesson 3 Homework Practice Surface Area Of Rectangular Prisms Answers
Divina Taton
Lesson 3 Homework Practice Surface Area Of Rectangular Prisms Answers
In this lesson, you will learn how to find the surface area of rectangular prisms using nets. A net is a two-dimensional figure that can be folded to form a three-dimensional solid. The surface area of a solid is the sum of the areas of all its faces.
How to find the surface area of a rectangular prism using a net
To find the surface area of a rectangular prism using a net, follow these steps:
Lesson 3 Homework Practice Surface Area Of Rectangular Prisms Answers
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- Identify the dimensions of the rectangular prism. The dimensions are the length, width, and height of the prism.
- Draw a net of the rectangular prism. The net consists of six rectangles: two congruent rectangles for the top and bottom faces, and four congruent rectangles for the lateral faces. The dimensions of each rectangle are determined by the dimensions of the prism. For example, if the prism has a length of l, a width of w, and a height of h, then the top and bottom rectangles have dimensions l by w, and the lateral rectangles have dimensions h by w.
- Find the area of each rectangle in the net. The area of a rectangle is given by multiplying its length by its width.
- Add up the areas of all the rectangles in the net. This is the surface area of the rectangular prism.
Example
Find the surface area of the rectangular prism below using its net.
Solution:
- The dimensions of the rectangular prism are 5 cm, 3 cm, and 4 cm.
- The net consists of six rectangles: two rectangles with dimensions 5 cm by 3 cm for the top and bottom faces, and four rectangles with dimensions 4 cm by 3 cm for the lateral faces.
- The area of each rectangle in the net is given by multiplying its length by its width. The areas are:
- Top and bottom rectangles: 5 cm x 3 cm = 15 cm
- Lateral rectangles: 4 cm x 3 cm = 12 cm
- The surface area of the rectangular prism is the sum of the areas of all the rectangles in the net. The surface area is:
15 cm + 15 cm + 12 cm + 12 cm + 12 cm + 12 cm
= 78 cm
Practice questions
Try these practice questions to test your understanding of finding the surface area of rectangular prisms using nets.
- Find the surface area of the rectangular prism below using its net.
- Find the surface area of the rectangular prism below using its net.
- A cereal box has dimensions of 20 cm by 10 cm by 30 cm. What is its surface area?
Conclusion
In this lesson, you learned how to find the surface area of rectangular prisms using nets. You also practiced some problems involving this skill. Remember that finding the surface area of a solid can help you measure how much material is needed to cover it or how much paint is needed to paint it. You can use nets to visualize how a solid can be unfolded into a two-dimensional figure and then find its surface area by adding up the areas of its faces.
Why is finding the surface area of rectangular prisms important?
Finding the surface area of rectangular prisms is an important skill that can help you in many real-world situations. For example, you may need to find the surface area of a rectangular prism if you want to:
- Wrap a gift box or a package.
- Cover a wall or a floor with tiles or wallpaper.
- Paint a room or a fence.
- Calculate the amount of material needed to make a tent or a book cover.
- Estimate the heat loss or gain of a building or a container.
In all these situations, finding the surface area of rectangular prisms can help you plan, budget, and optimize your resources.
How to check your answers for finding the surface area of rectangular prisms
After you find the surface area of rectangular prisms using nets, you may want to check your answers to make sure they are correct. One way to check your answers is to use the formula for the surface area of rectangular prisms. The formula is:
S = 2lw + 2lh + 2wh
where S is the surface area, l is the length, w is the width, and h is the height of the prism.
To use the formula, you need to know the dimensions of the prism. You can find them by looking at the net or the prism itself. Then, you plug in the values into the formula and simplify. If your answer matches the one you got using nets, then you are correct. If not, then you may have made a mistake somewhere and need to review your work.
For example, let's check the answer for the example we did earlier using nets. The dimensions of the prism were 5 cm, 3 cm, and 4 cm. The surface area we got using nets was 78 cm. Using the formula, we get:
S = 2lw + 2lh + 2wh
S = 2(5)(3) + 2(5)(4) + 2(3)(4)
S = 30 + 40 + 24
S = 94
This matches the answer we got using nets, so we are correct.
How to find the surface area of rectangular prisms without using nets
Sometimes, you may not have a net of a rectangular prism or you may not want to draw one. In that case, you can still find the surface area of rectangular prisms without using nets. You just need to use the formula for the surface area of rectangular prisms and know the dimensions of the prism.
The formula for the surface area of rectangular prisms is:
S = 2lw + 2lh + 2wh
where S is the surface area, l is the length, w is the width, and h is the height of the prism.
To use the formula, you need to know the dimensions of the prism. You can find them by looking at the prism itself or by measuring it with a ruler. Then, you plug in the values into the formula and simplify. This will give you the surface area of the rectangular prism.
Example
Find the surface area of the rectangular prism below without using nets.
Solution:
- The dimensions of the rectangular prism are 5 cm, 3 cm, and 4 cm.
- Using the formula for the surface area of rectangular prisms, we get:
S = 2lw + 2lh + 2wh
S = 2(5)(3) + 2(5)(4) + 2(3)(4)
S = 30 + 40 + 24
S = 94
- The surface area of the rectangular prism is 94 cm.
Practice questions
Try these practice questions to test your understanding of finding the surface area of rectangular prisms without using nets.
- Find the surface area of the rectangular prism below without using nets.
- Find the surface area of the rectangular prism below without using nets.
- A cardboard box has dimensions of 25 cm by 15 cm by 20 cm. What is its surface area?
Conclusion
In this lesson, you learned how to find the surface area of rectangular prisms without using nets. You also practiced some problems involving this skill. Remember that finding the surface area of a solid can help you measure how much material is needed to cover it or how much paint is needed to paint it. You can use the formula for the surface area of rectangular prisms to find it quickly and easily if you know the dimensions of the prism.
How to find the surface area of rectangular prisms using a shortcut
If you are familiar with the formula for the surface area of rectangular prisms, you may notice that it involves adding up six terms: two for each pair of opposite faces. However, there is a shortcut that can help you find the surface area of rectangular prisms faster and easier. The shortcut is to add up the areas of only three faces and then multiply by two.
The reason this shortcut works is because the opposite faces of a rectangular prism are always congruent, meaning they have the same shape and size. Therefore, their areas are also equal. So, instead of adding up the areas of all six faces, you can just add up the areas of three faces and then double it to get the same result.
To use this shortcut, you need to know the dimensions of the prism. You can find them by looking at the prism itself or by measuring it with a ruler. Then, you choose any three faces that share a vertex (a corner point) and find their areas by multiplying their lengths and widths. Then, you add up those areas and multiply by two. This will give you the surface area of the rectangular prism.
Example
Find the surface area of the rectangular prism below using the shortcut.
Solution:
- The dimensions of the rectangular prism are 5 cm, 3 cm, and 4 cm.
- Choose any three faces that share a vertex. For example, we can choose the front face, the right face, and the top face.
- Find the area of each face by multiplying its length and width. The areas are:
- Front face: 5 cm x 4 cm = 20 cm
- Right face: 4 cm x 3 cm = 12 cm
- Top face: 5 cm x 3 cm = 15 cm
- Add up the areas of the three faces and multiply by two. The surface area is:
(20 + 12 + 15) x 2
= 94
- The surface area of the rectangular prism is 94 cm.
Practice questions
Try these practice questions to test your understanding of finding the surface area of rectangular prisms using the shortcut.
- Find the surface area of the rectangular prism below using the shortcut.
- Find the surface area of the rectangular prism below using the shortcut.
- A chocolate bar has dimensions of 10 cm by 4 cm by 1 cm. What is its surface area?
Conclusion
In this lesson, you learned how to find the surface area of rectangular prisms using a shortcut. You also practiced some problems involving this skill. Remember that finding the surface area of a solid can help you measure how much material is needed to cover it or how much paint is needed to paint it. You can use the shortcut to find it quickly and easily if you know the dimensions of the prism and remember that opposite faces have equal areas.
Summary
In this article, you learned how to find the surface area of rectangular prisms using different methods. You learned how to use nets, formulas, and shortcuts to calculate the surface area of rectangular prisms. You also learned why finding the surface area of rectangular prisms is important and how to check your answers. You practiced some problems involving finding the surface area of rectangular prisms using nets, formulas, and shortcuts.
By reading this article, you have completed Lesson 3 Homework Practice Surface Area Of Rectangular Prisms Answers. You have mastered the skill of finding the surface area of rectangular prisms using various methods. You can apply this skill to many real-world situations that involve measuring the size of 3D objects. You can also use this skill to prepare for more advanced topics in geometry, such as finding the surface area of other solids.
We hope you enjoyed this article and learned something new. If you have any questions or feedback, please leave a comment below. Thank you for reading and happy learning!
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