If you think you can figure it out, triangles are not so bad. But what about triangles?' Well, once again pause the video I can get a square, I can get a rectangle. 'Ok, that's not so hard to digest, that if I intersect a plane with a cube, That magicians use to saw people in half, or pretend like they are - they give us the illusion of sawing people in half, it might look something like this. If you imagine the plane just like one of those huge blades Let me shade in the stuff, if you kind of view this, So it might look like this, and once again That I'm cutting with, and my cube is going to beĪ rectangle. That I'm actually cutting with, so the intersection of the plane That you are cutting with so, the intersection, let's see: This could be the plane

Right over there, then the intersection of the plane I think you'd see where this is going, this side like that, and then you cut the bottom, You can actually cut like this: So, if you cut this side like this, and then cut that side like that, and then you cut this side like that That I'm talking about? Well for a rectangle On your own: How can you get these shapes How can you get that? And at any point, I encourage you: Pause the video and try to think about it So a square isĪ pretty straightforward thing to get, if you're doing a planar slice of a cube. it could look something like this.Īnd I can even color in the part of the plane that you couldĪctually see it the cube were opaque, if you couldn't see through it.īut if you could see through it you would see this dotted line,Īnd the plane would look like that. Let me see if I can do a decent,Īs you see you'd say a part of the plane, that is cutting this cube. So you can imagine a plane that did this, and if I wanna draw the broader plane, Of the glass cube, where you will see it, right over there, dotted line, and then it cuts this, right over here. We are to cut, just like this, the square is maybe the most obvious one, so it cuts the top right over there, it cuts the side, right over here, it cuts the side, I guess on the back To get the intersection of this cube, and that plane to be a square? We'll imagine that that plane So what am I talking about? Let's say we wanna deconstruct a square: How can we slice a cube with a plane Is explore the types of 2D shapes we can construct,īy taking planar slices of cubes.

Trapezoid prism volume khan academy