 Hello Geometricians. We're heading into the final stretch. We're starting chapters 12 and 13 which are three-dimensional geometry properties. We're going to be talking about surface area and volume. But before we get into that I want to talk a little bit about nets. Back in seventh grade or eighth grade maybe you call them flat patterns, but on standardized tests they're called nets. So we're going to refer to them as nets. The net you see here is a net for a cube. It has six faces. All of them are squares. And when I fold it up you will see that it folds into a cube. The purple surfaces are the lateral area. The green are the bases. The bases are always opposite each other. And so that flat pattern or that net folds into a cube. So that net folds into a cube. Do you think this net would fold into a cube? Do you think this net would fold into a cube? This one would not fold into a cube because while you would have your four purple sides and the green base covered this other green base is not in a position to top off the cube. So that flat pattern does not fold into a cube. Would this fold into a cube? I think it would. I think this base would have these purple lateral faces again to make the sides. And then the green face here and makes the opposite base. The four purple lateral faces are there. It is a cube. There are several arrangements of the six squares that make cubes and several arrangements that do not make cubes. It might be interesting for you to research that on the internet how many different arrangements of the six faces fold into an accurate cube. Check with your teacher. It might be kind of a fun little thing to research. Now I have a completely different arrangement. I have a green base and four purple lateral faces. What shape do you think will happen when I pull this all together? It does not have two bases. It only has one base. When I pull it up and let everything magnetize together, it turns into a pyramid. I have got one square base and four triangular lateral faces. That would be a square pyramid or a rectangular pyramid. What shape will this make? I have got two green bases. They are triangles and three purple lateral faces. When I fold it all together the two green triangular faces hook up with the two faces. The lateral surfaces are rectangular in shape. The bases are triangles. One of the words we would use to name this would be triangular. Because it has two faces it is a prism. This is a flat pattern, a net for a triangular prism. When it folds up it makes a prism. It has got two bases. The shape of the bases is a triangle. What shape will this make? Again I have one base and the lateral faces are triangles again. When that happens I am going to have a pyramid. This folds into a pyramid. I have one base. The shape of the base is a triangle. I have three purple lateral faces. It is a triangular pyramid. It is a very possible combination of shapes. Look at this shape and think about what you think that will fold into. It does fold in accurately. The bases, the flaps, whatever you want to call them everything is organized in the right kind of way. If you think of these two opposite flaps as bases this folds into a rectangular prism. An awkward one. But a rectangular prism nonetheless. One of the dimensions is a one. The other dimension is a two. I don't have it written on the base. The height of the prism is four. The distance between the two bases is four. This is a flat pattern for a rectangular prism. What is this a flat pattern for? I'm sorry, a net for. I've got a diameter. I've got a radius. I've got a three. The three will be the distance between the two bases. This is not a polyhedron. Because it has curved surfaces it's not a polyhedron. But this will fold into, I would loosely call it a can. I would technically call it a cylinder. A cylinder with a base of radius one. If the radius is one then the diameter is two. The height of the cylinder the distance between the bases is three. It will be interesting for you to think about how you would get this distance. When we find surface area we're going to want to know the area of that rectangle. And we've got the three. That's the distance the other dimension of that rectangle. We'll be talking about this in a couple of days. The first day of the unit is building three-dimensional objects. So you'll be using the skills you've developed about nets in the second day of the unit. It's going to be great fun. You're going to love three dimensions.