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### Course: Grade 7 (VA SOL) > Unit 7

Lesson 1: Nets of 3D figures# Surface area of a box using nets

Discover the surface area of a cereal box by visualizing a net. Cut and flatten the box to create a 2D shape. Measure the dimensions, calculate the area of each section, and add them up for the total surface area. Fun and practical!

## Want to join the conversation?

- You don't have to use a net. S=2lw+2wh+2lh(38 votes)
- Or 2(lw+wh+lh)(47 votes)

- At1:31is he drawing in the height?(11 votes)
- Sort of, he is drawing what cannot be seen, the height of the back of the cereal box. Dotted lines mean behind the shape.(6 votes)

- this is hard can some one help(9 votes)
- If you find this method hard, try the previous video.

Or use the formula 2(lb+bh+lh)

where l is length , b is breadth and h is height.(14 votes)

- Ok, here's a question. Why do we need the use of nets in real life? Is it just the standard they added to extend school? BTW: Sal makes me want to learn more about cereal boxes and math :-)(9 votes)
- Most boxes are flat when they are produced, think of pizza boxes, the ppl at the pizza shops fold the boxes. They need to know the dimensions to order the proper sizes.

When building Wood Framed Structures usually the walls are made on the ground first then lifted up into position. so the "net" is made first before the building takes shape(5 votes)

- Why can’t you just multiply height times width times base?(6 votes)
- If you multiply these three, you are finding the volume, not surface area.(9 votes)

- How do you do this again(5 votes)
- Imagine that you are unfolding a polyhedron to be flat.

It might help to draw what that looks like, you might need to practice a few times, but you should get a hang of it.

After you have the net of your polyhedron, then find the area by breaking it down into shapes that you know how to take the area of, such as rectangles and triangles.

Then, add the total area together to get your answer, which is equal to the surface area of the polyhedron.(10 votes)

- Wait how did he get 60cm, when u measure a rectangle, you multiply length times width but he included also one more dimension. Why??(2 votes)
- Why did he right the back of the box at the bottom?(2 votes)
- how do u multiply it?(1 vote)
- Congrats on getting it(1 vote)

## Video transcript

- [Instructor] In a previous
video, we figured out how to find the surface
area of this cereal box by figuring out the areas
of each of the six surfaces of the box and then adding them all up. I'm gonna do that again in this video, but I'm gonna do it by
visualizing a net for the box. And the way I think about
a net of a box like this is what would happen if you
were to, if you were to, if you were to cut the cardboard and then flatten it all out. So what am I talking about? Well, what we have here, we could imagine making a cut in the box and the cut could be, see,
I could make a cut back here so I could make a cut right over there. I could cut it. I could cut it right like this. I could cut it like that. So if I just did that, this
top flap would flap open. So that would be able
to come out like that. And then I could also
make a cut for this side so I can make a cut back there. And I could make a cut right over here. And now this side could flap forward, and I could do the same thing on this other side right over here. Then that could flap forward. And then the backside, I could draw it. So I would also have a cut,
I'll draw it as a dotted line. 'Cause you're not be able to,
you're not supposed to be able to see this cut, but the corresponding cut to this one on this
side that we can't see. Lemme draw it a little
bit neater than that. The corresponding cut
would be right back here, right back there. And then a cut right over here. And so what would happen if we were to flatten all of this out? Well, we would have the front of the box. I'll try to draw this as neatly as I can. So the front of the box looks like this. We would have this top
flap, which looks like this. If we were to flatten it all out, we have these two side flaps. So that's a side flap. That's a side flap. And this is another, this
side flap right over here. That's a side flap. Then we would have the bottom of the box. So the bottom of the box
is gonna look like this, bottom of the box. And then we have the back of the box that the bottom is going to be connected to, we didn't cut that. So that we have the back of the box. The back of the box looks like this. And there we have it. We've made the net. This is what would happen if you made the cuts that I talked about and then flatten the box out. It would look like this. Now how could we use this net to find the surface area? Well, we just need to
figure out the surface area of this shape now. So how do we do that? Well, we know a lot about the dimensions. We know that this width right over here, that this is 10 centimeters. 10 centimeters from there to there. We know the height
actually going all the way from here all the way up, because the height of the
box is 20 centimeters. So this is going to be 20
centimeters, right over here, then you have another 20 centimeters, you have another 20
centimeters right over here and right over here if you like. And then you have, see the depth of the box is three centimeters. So this is three centimeters.
Three centimeters. And then this is three centimeters. And so what is the area, actually, let me just do one region first. What is the area of this
entire region that I am, that I am shading in with this blue color? Well, it's 10 centimeters. That is, I'll do a color that you can see a little bit more easily. It is 10 centimeters wide. 10 centimeters, times, what's the height? 20 plus three plus 20 plus three. So that's going to be 40 plus six. So times 46 centimeters. That's this blue area. So that's gonna be 460 square centimeters, 460 square centimeters. And now we just have
to figure out the area of the two flaps. So this flap right over
here is 20 centimeters by three centimeters, so
that's 60 centimeters squared. So 60 centimeters squared, or 60 square centimeters I should say. And then this flap is gonna
have the exact same area, another 60 square centimeters,
60 square centimeters. And you add everything together. We deserve a little bit of a drum roll. We get, well this is gonna add up to 580 square centimeters, which is the exact thing
we got in the other video where we didn't use a net. And you should just, it's nice to be able to do it either way to be
able to visualize the net or be able to look at this and think about the different
sides, even the sides that you might not necessarily see.