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ISTEP+ Grade 7 - Math: Test Prep & Practice22 chapters | 171 lessons | 8 flashcard sets

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you'll learn how you can create your own nets to make your own rectangular prism boxes for gifts. You'll also learn how you can figure out how much gift wrapping you'll need.

Your friend has just graduated from college and you want to give him a very special gift. Your friend just happens to love old style pens, so you have purchased him a 100 year old fountain pen. Now, you need to make a box to fit the pen. You don't want the pen to be flopping around, so it needs to fit the pen well. The pen comes with a stand, so it needs to be big enough to hold the stand as well.

To make your box, you begin by constructing a net of the box. This **net** is what you get when you unfold the sides of the box so it's all flat. You can also begin with a net and fold it into a box. To make your net, you remember that your box needs to have a total of 6 sides. You decide to make a net where the bottom is surrounded by its four sides and then the top connected to one of the sides.

This net of the box that you are making is also called a **right rectangular prism**, basically a rectangular box. A prism is a solid piece, whereas your box is hollow. The resulting net from both shapes is the same, however.

Once you have your net, you can now go ahead and form it. To form it, you bend your net at all the edges. Once you've bended all the edges, it will take the shape of your box or right rectangular prism.

The two little rectangles of your net have become your left and right sides of the box. The long rectangles have become your bottom, your top, and your front and back sides.

Now that you have your rectangular prism box, you now need to figure out how much wrapping paper you'll need to wrap it. To figure this out, you'll actually be figuring out the surface area of your prism, your box. Since you have your net, it actually makes your job that much easier. You can use your net and its dimensions to calculate your surface area. All you have to do is to figure out the individual areas of your rectangles and add them up to find the surface area of your right rectangular prism box.

Here are the dimensions for your net.

You can see that you have 4 rectangles that measure 10 x 5 inches and two rectangles that measure 5 x 5 inches. You remember the formula for the area of a rectangle is length times width, so you go ahead and multiply your dimensions together. You get 10 x 5 = 50 and 5 x 5 = 25. There are 4 rectangles with an area of 25 and 2 rectangles with an area of 25, so your total surface area is 4 * 50 + 2 * 25 = 250 square inches.

Let's look at another example. Here is a net of another right rectangular prism. What is the surface area for this prism?

To find the surface area of this prism, you again find the areas of the rectangles that make up his net and then you add them all up. This is what you get.

- 3 * 8 = 24, you have 2 of these
- 6 * 8 = 48, you have 2 of these
- 3 * 6 = 18, you also have 2 of these

Adding these all up, you get this.

- 2 * 24 + 2 * 48 + 2 * 18 = 180 square inches

This particular prism has a surface area of 180 square inches. That's how much wrapping paper you would need to wrap this prism up.

Let's review.

A **net** is what you get when you unfold the sides of a box so it's all flat. In this lesson, you learned about the net of a **right rectangular prism**, basically a rectangular box.

You learned that to find the surface area of a right rectangular prism, all you need to know are the dimensions of the various sides of your net. You find these individual areas and then you add them all up.

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9 in chapter 17 of the course:

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ISTEP+ Grade 7 - Math: Test Prep & Practice22 chapters | 171 lessons | 8 flashcard sets

- Planes and the Polyhedron: Definition and Example 3:52
- What Are Platonic Solids? - Definition and Types 4:39
- Overview of Three-dimensional Shapes in Geometry 3:28
- How to Find Surface Area of a Cube and a Rectangular Prism 4:08
- How to Find Surface Area of a Cylinder 4:26
- How to Find Surface Area of a Pyramid 5:11
- Volume of Prisms and Pyramids 6:15
- Volume of Cylinders, Cones, and Spheres 7:50
- Constructing & Measuring Right Rectangular Prisms From Nets
- Go to ISTEP+ Grade 7 Math: Complex Figures

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