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## Lesson 13: Polyhedra

Current time:0:00Total duration:3:47

# Counting faces and edges of 3D shapes

## Video transcript

- [Instructor] 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, and I'll see if we can
work through it together. And I'm gonna actually
try to color the faces. So, we have this face over, whoops, let me do it
in my, this other tool, so we 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 gonna be our fourth face. That's going to be our fourth face. And then 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 is the face, there's, 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, we're gonna 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 gonna 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 'cause 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 of here, which
is edge number eight. And I actually found this
very valuable to color 'em 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 that'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.