Counting faces and edges of 3D shapes

How many faces does the following shape have? Pause this video and see if you can figure that out.

All right, I'm assuming you paused it, and I'll see if we can work through it together. I'm going to actually try to color the faces. So, we have this face over—oops, let me do it in my—this other tool.

So you have this face over here in the back, so that's one face. So that's one. Then, you have this face right over here, also in the back. The only way we can see this is because they've drawn it so that it is transparent. So that is the second face.

Now you have this triangular face on top, so let me color that in. So you have this triangular face on top, so that's going to be our third face. Third face, and then you have this triangular face on the bottom. That's going to be our fourth face. That's going to be our fourth face.

And the key question is, are we done? Looks like I've colored all the ones that I can see, but there's one a little bit tricky here. There's the one that we are actually seeing through. There's the face—let me pick a color. There's the face out front that we can see through so that we can see faces one, two, and four. So that's actually going to be our fifth face. The way they've drawn it, it's like it's made out of glass so we can see faces one, two, and four. But that is our fifth face.

And so this thing has five faces. All right, let's do another example, but instead of faces, let's think about—we're going to think about edges. So how many edges does the following shape have? Pause the video and see if you can work through this.

Okay, let's work through this together now, and I'm just going to count these edges. So the edges are where two faces meet. So this is an edge right over there. So that's one edge. There's an edge back here—we can see because it's transparent—that is our second edge. We have this one over here; that is our third edge. We have this one over there; that is our fourth edge. Then we have this one over here; that is our fifth edge.

Now, we have this here. This is our sixth edge. Let's see—all we have left is this one, which is edge number seven. And then last but not least, this edge over here, which is edge number eight. I actually found this very valuable to color them in to make sure that I wasn't missing an edge or double counting an edge.

So this thing has eight—eight edges. Actually, if you're curious, just for extra practice, how many faces does this have? Well, we can count those as well. This has one face back there, another face back there, so it's two faces.

And then, you have a third face, which is the base—this rectangular face. So that's three faces. And then you have your two faces out front. You have this face that we're seeing through, and then we have that face that we're seeing through. So even though they're asking edges, just for practice, we figured out that this thing has five faces, one for the square base, and then four triangular faces for these sides to make this square pyramid.

So it has eight edges and five faces.