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Lesson 3 Homework Practice Surface Area Of Rectangular Prisms 🟤

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Lesson 3 Homework Practice Surface Area Of Rectangular Prisms

In this lesson, you will learn how to find the surface area of rectangular prisms. A rectangular prism is a three-dimensional shape that has six rectangular faces. The surface area of a rectangular prism is the total area of all its faces. Finding the surface area of rectangular prisms is useful for many real-life situations, such as wrapping a gift box, painting a wall, or building a fence.

Surface Area Formula for Rectangular Prisms

To find the surface area of a rectangular prism, you need to know its length, width, and height. These are the dimensions of the prism that measure how long, wide, and tall it is. You can label these dimensions as l, w, and h on a diagram of the prism.

A diagram of a rectangular prism with dimensions labeled as l, w, and h

The surface area formula for rectangular prisms is:

Surface area = 2lw + 2wh + 2lh

This formula tells you to add up the areas of all six faces of the prism. Each face is a rectangle, so its area is found by multiplying its length and width. There are two faces with dimensions l and w, two faces with dimensions w and h, and two faces with dimensions l and h. That’s why you multiply each pair of dimensions by 2 in the formula.

How to Find the Surface Area of Rectangular Prisms

To use the surface area formula for rectangular prisms, follow these steps:

  1. Identify the length, width, and height of the prism and label them as l, w, and h.
  2. Plug these values into the formula: Surface area = 2lw + 2wh + 2lh.
  3. Simplify the expression by multiplying and adding.
  4. Write your answer with the correct units squared.

Let’s see an example of how to apply these steps.

Example

Find the surface area of a rectangular prism that has a length of 10 cm, a width of 6 cm, and a height of 4 cm.

Solution

Step 1: Identify the length, width, and height of the prism and label them as l, w, and h.

We are given that l = 10 cm, w = 6 cm, and h = 4 cm.

Step 2: Plug these values into the formula: Surface area = 2lw + 2wh + 2lh.

Surface area = 2(10)(6) + 2(6)(4) + 2(10)(4)

Step 3: Simplify the expression by multiplying and adding.

Surface area = 120 + 48 + 80

Surface area = 248

Step 4: Write your answer with the correct units squared.

The units are centimeters, so we write cm. The final answer is:

Surface area = 248 cm

Surface Area Word Problems for Rectangular Prisms

One way to practice finding the surface area of rectangular prisms is to solve word problems that involve real-life situations. Word problems can help you understand how to apply the surface area formula to different scenarios and contexts. Here are some tips to help you solve surface area word problems for rectangular prisms:

  • Read the problem carefully and identify the given information and the question.
  • Draw a diagram of the rectangular prism and label its dimensions with the given information.
  • If any dimension is missing, use the given information to find it.
  • Plug the dimensions into the surface area formula and simplify.
  • Write your answer with the correct units squared and check if it makes sense.

Let’s see an example of how to solve a surface area word problem for a rectangular prism.

Example

A cereal box has a length of 20 cm, a width of 10 cm, and a height of 30 cm. How much cardboard is needed to make the box?

Solution

Step 1: Read the problem carefully and identify the given information and the question.

We are given that l = 20 cm, w = 10 cm, and h = 30 cm. We are asked to find the surface area of the box.

Step 2: Draw a diagram of the rectangular prism and label its dimensions with the given information.

A diagram of a rectangular prism with dimensions labeled as l = 20 cm, w = 10 cm, and h = 30 cm

Step 3: If any dimension is missing, use the given information to find it.

We have all the dimensions, so we can skip this step.

Step 4: Plug the dimensions into the surface area formula and simplify.

Surface area = 2lw + 2wh + 2lh

Surface area = 2(20)(10) + 2(10)(30) + 2(20)(30)

Surface area = 400 + 600 + 1200

Surface area = 2200

Step 5: Write your answer with the correct units squared and check if it makes sense.

The units are centimeters, so we write cm. The final answer is:

Surface area = 2200 cm

This answer makes sense because it is positive and reasonable for a cereal box.

Conclusion

In this lesson, you learned how to find the surface area of rectangular prisms. You learned the surface area formula for rectangular prisms and how to use it with different dimensions. You also learned how to solve word problems that involve finding the surface area of rectangular prisms in real-life situations. Finding the surface area of rectangular prisms is an important skill that can help you with many practical applications, such as wrapping, painting, or building. You can practice finding the surface area of rectangular prisms by using worksheets, online calculators, or 3D models. By doing so, you will improve your geometry and problem-solving skills.

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