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Current time:0:00Total duration:6:48

CCSS.Math:

what we're going to explore in this video er polyhedra polyhedra which is just the plural of a polyhedron and a polyhedron is a three-dimensional shape that has flat surfaces and straight edges so for example a cube is a polyhedron a cube is a polyhedron all the surfaces are flat all the surfaces are flat and all of the edges all of the edges are straight so this right over here is a polyhedron once again polyhedra is plural polyhedron is when you have one of them this is a polyhedron a rectangular pyramid is a polyhedron so let me draw that I'll make this one a little bit more transparent let me do this in a different color just for fun I'll make it a magenta rectangular pyramid so once again here I have one flat surface and then I'm going to have four four triangular flat surfaces so this right over here this is a rectangular pyramid now it's clearly looks like a pyramid why is it called a rectangular pyramid because the base right over here is a rectangle so these are just a few examples of polyhedra now what I want to think about our Nets of polyhedron actually let me draw and make this transparent too so we get full appreciation of the entire polyhedra polyhedron this entire cube so now let's think about Nets of polyhedron nets so what is a net of a polyhedron well that one way to think about is if you kind of view this as made up of cardboard and you were to unfold it in some way so it would become flat or another way of thinking about it is if you were to cut out some cardboard or some paper and you wanted to fold it up into one of these figures how would you go about doing it and each of these polyhedra has multiple different nets that you could create so it can be folded up into this three-dimensional figure so let's let's take an example and maybe the simplest example would be a cube like this and I'm going to color code it so let's say that the bottom of this cube the bottom of this cube was this green color and I can represent it like this that's the bottom of the cube it's that green color now let's say that this back surface of the cube is orange well I could represent it like this and notice I've kind of folded it out I'm folding it out and so if I were to flatten it out it would look like this would look like that now this other backside I'll shade it in yellow this other backside right over here I could fold it backwards and keep it connected along this edge keep it connected along this edge fold it backwards it would look like this it would look like that I think you get the general idea here and just to make clear this edge right over here is this edge right over there now I have to worry about this top part the top part of the cube maybe it is in let me do it in a pink color this top part of the cube is in this pink color and it needs to be attached to one of these sides I could attach it to this side or this side let's attach it over here so let's say it's attached to that yellow side back here so then when we fold it out when we really unpack the thing so we folded that yellow part back that we're folding this part back then it would be right over here it would be right over there and then we could fold we could fold this front face this front face right over here we could fold that out and this along this edge and it would go right over there it would go right over there and then we have one face of the cube left we have this side right over here and we could what we could do actually several things we could fold it out along this edge and then we would draw the key we would draw the surface right over there or or if we want to do something interesting we could fold it out we could fold this out along the edge that shares with the yellow that back side so we could fold it out like this so if we folded it out like this it would be connected to the yellow square right over here so you see that there's many many ways there's many many ways to construct a net or a net that when you fold it all back up will turn into this polyhedron in this case a cube let's do one more example let's do the rectangular pyramid because all of these had all of these head rectangles are in particular this had squares as our surfaces now the most obvious one might be to start with your base right over here start with your base and then take the different sides and then just fold them straight out so for example we could take this side right over here fold it out and it would look like it would look like that we could take this side back here and once again just fold it out fold it fold it out it would look like that it should be the same size as that orange side but I'm hand drawing it so it's not going to be perfect so that's that right over there and then you could take this front side right over here and once again fold it out along this edge so it would look like this and then finally you could take this side right over here and once again fold it out along this edge and it would go right there but this isn't the only net for this rectangular pyramid there's other options for example and just to explore one of them instead of folding that green side out that way instead instead we might have wanted to fold it out along this edge along this edge with the yellow side that you can see actually let's make it a little bit different let's fold it out along this side since we can see the edge and let me label let me color the edge so this is the edge right over here on the blue triangle so this is the edge when you fold the green triangle out it would look like this if you fold the green triangle out it would look like this so hopefully this gives you an appreciation this gives you appreciation there's multiple ways to unfold these three-dimensional figures these polyhedra or multiple ways to if you wanted to do a cardboard cutout and then fold things back together to construct them and these flattened versions of them these things these these these unpacking of these polyhedra we call nets