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# Surface area of a box using nets

CCSS.Math:

## Video transcript

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 going to do that again in this video but I'm going to 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 can 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 back side and I could I could draw it so I would also have a cut I'll draw it as a dotted line because you're not be able 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 we 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 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 going to look like this bottom of the box and then we have the back of the box at the bottom is going to be connected to we didn't we didn't cut that so 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 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 3 centimeters so this is 3 centimeters 3 centimeters and then this is 3 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 it in 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 3 plus 20 plus 3 so that's going to be 40 plus 6 so times 46 centimeters that's this blue area so that's going to be 460 460 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 3 centimeters so that's 60 centimeters squared so 60 centimeters squared or 60 square centimeters I should say and then this flap is going to have the exact same area another 60 square centimeters 60 square centimeters and you add everything together we deserve a little bit of a drumroll we get well this is going to add up to 500 and eighty square centimeters which is the exact thing we got in the other video where we didn't use the 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 and think about the different sides even the sides that you might know that so not necessarily see