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### Course: 6th grade (Illustrative Mathematics) > Unit 1

Lesson 8: Lesson 13: Polyhedra# Counting faces and edges of 3D shapes

Learn about shapes! Discover how to count faces and edges on 3D figures. We explore a transparent shape with five faces and another shape, a square pyramid, with eight edges and five faces. It's a colorful journey into geometry!

## Want to join the conversation?

- are vertices the same as edges(17 votes)
- No, vertices are like corners where three faces meet, with the exception of the apex, in which 4 or more faces meet in a pyramid.(31 votes)

- how can i identify faces and edges of a sphere? maybe its silly to ask but i am curious.(6 votes)
- A face is a flat surface on a solid, and edges are the lines at which faces meet, and a vertex is the point at which when three or more edges meet. A sphere has no flat surfaces, so it has no faces. Since it doesn't have faces, it can't have edges, or vertices.(14 votes)

- can a 3d shape have 4 faces?(2 votes)
- Yes it can have 4 faces. I am pretty sure I am correct.(1 vote)

- What about parallelograms and(2 votes)
- So this video really made me better.(2 votes)
- Is cylinder a prism? Is cone a pyramid?(1 vote)
- no because all of the faces of prisms and pyramids have to be polygons.(2 votes)

- hey sister what is angle(1 vote)
- Hey!
*(Credit to Dictionary.com)*An angle is a geometric figure formed by two lines that begin at a common point or by two planes that begin at a common line.(2 votes)

- how do i count the faces(2 votes)
- just count the number of closed shapes,but remember that there could be one that is see-through.(0 votes)

- Do we have to add up all the sides together?(2 votes)
- Yes. If you want to find the total number of sides or the surface area of some shapes (cube), then yes.(0 votes)

- Can you multiply the number of sides you have to get the number of edges and vertices you have respectively?(2 votes)
- It won’t work in may case like in a triangle.(0 votes)

## 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 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 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. And that's going to be our fourth face. And then the key question is, are we done? It 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,
there's, let 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 gonna think about, 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 over 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.