20 consider a pyramid whose base is a regular n gonthat is a...

Consider a pyramid whose base is a regular n-gon—that is, a regular polygon with n sides. How many vertices would such a pyramid have? How many faces? How many edges? (a) Describe the relationship between the number of vertices of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has n + 1 more vertices than an n-gon pyramid. An n-gon prism has n − 2 more vertices than an n-gon pyramid. An n-gon prism has n more vertices than an n-gon pyramid. An n-gon prism has n − 1 more vertices than an n-gon pyramid. An n-gon prism has n + 2 more vertices than an n-gon pyramid. (b) Describe the relationship between the number of faces of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has one more face than an n-gon pyramid. An n-gon prism has two fewer faces than an n-gon pyramid. An n-gon prism has two more faces than an n-gon pyramid. An n-gon prism has one less face than an n-gon pyramid. An n-gon prism has the same number of faces as an n-gon pyramid. (c) Describe the relationship between the number of edges of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has n − 1 more edges than an n-gon pyramid. An n-gon prism has n − 2 more edges than an n-gon pyramid. An n-gon prism has n more edges than an n-gon pyramid. An n-gon prism has n + 2 more edges than an n-gon pyramid. An n-gon prism has n + 1 more edges than an n-gon pyramid.

Transcript

00:01 All right, so i'm going to give this one a go.

00:03 I hope i read it correctly.

00:06 So we're going to consider a pyramid whose base is a regular polygon with n number of sides.

00:12 Okay, how many vertices would the pyramid have, how many faces, how many edges, blah, blah, blah.

00:17 A says, describe the relationship between the number of vertices of an n -gone prism and an end -gone pyramid.

00:27 Okay.

00:28 So let's kind of, let me draw some pictures here.

00:31 Here's the pyramid.

00:33 We have some polygon.

00:35 Pick a number of sides.

00:37 It doesn't matter how many sides.

00:38 Pick a number of sides.

00:39 If we only have three sides for our base, our base is maybe a triangle, right? so there's the base in red, and then it goes to a point because it's a pyramid like that.

01:01 This back line would be dotted because it's behind all the walls and stuff.

01:10 Okay, so there's our pyramid.

01:14 So if you notice, the base has three pyramids, which is the same as the number of sides, and then this point on the top is one more.

01:25 So in a pyramid, however many vertices we have for the base, which is how many sides we have, so here the number of vertices is going to be the number of sides end plus the way.

01:43 One vertices before the top.

01:46 Okay, there, you know, if i had a four -sided figure for a base, you know, square, it's supposed to be regular polygon.

02:00 You know, if i had four sides for the base, well, there's one, two, three vertices, but then remember it's a pyramid, so it goes to a point, which gives us another vertices.

02:13 Okay, so there's a pyramid.

02:15 So there's a pyramid.

02:15 So there's a there's the one, two, three, four vertices of the base plus the one more, which is, again, n plus one.

02:25 The number of vertices is the same as the number of bases.

02:29 Okay.

02:30 So then it says, describe the way between number of vertices of a prism and the number of vertices of an end -gone prism and the number of vertices on an end -gone pyramid.

02:43 Okay.

02:44 So that's the pyramid.

02:45 N plus one.

02:47 Okay.

02:49 Now, for a prism, let's do a different, let's do like a five -sided figure.

02:55 Why do i do this to myself? okay.

02:58 So a prism is, oh boy, i go like this.

03:10 That's too much, because these things are so easy to draw.

03:16 Just kidding.

03:24 So there's the base, and we're going to have the exact same thing up on the top.

03:29 And then we have the same shape.

03:30 And then we have the same shape.

03:31 On the top so these are the bases and then all of the vertices connect each other so this will connect it's behind everything to this this one comes straight down to here this one comes straight down to here that goes to there this goes to there right there so so there's our now these little these sides would be dotted because they're like in the background okay so so there's our prism.

04:12 So the prism, the base is the base, but then it goes to a point.

04:17 It doesn't go to a point.

04:18 It goes to another base.

04:21 So remember, our base is, in this case, five sides.

04:26 It's some n -sided polygons, n -sided regular polygon.

04:31 Well, if there's five, the number of vertices on the bottom are going to be n.

04:36 We're going to have the same number of vertices at the other bribes.

04:40 Base.

04:41 So here the vertices are 2n.

04:49 Okay.

04:50 So, so if we're wondering, the difference, you know, it looks like it's a multiple choice.

05:03 So the prism is going to have more.

05:07 It's going to have 2n.

05:09 The pyramid, it's going to be the number of size.

05:18 It's going to just be n.

05:19 It's going to plus 1 so if you compare the 2 in order to right so let's see prism is 2n pyramid is n plus 1 okay so if to make these the same i'm gonna have to add n i'm gonna up to the pyramid i'm gonna have to add an to make a 2n, but then i'm going to have to subtract 1.

06:00 So the prism has, right, to make these equal, i'm going to have to add an n and a minus 1.

06:09 So n minus 1, or the number of sides minus 1, that's how many more vertices the prism has than the pyramid.

06:24 So i'm hoping, because i didn't copy it off, so i would say that the prism, n -gom prism has, this is the one i would pick.

06:40 I think this is one of the choices.

06:43 Has n -minus -one more vertices than the pyramid.

07:05 Okay.

07:06 And so that's you find it.

07:08 That's what you do.

07:09 I don't know what the choices are.

07:12 And i think we're just, oops, i think it just said, look at the, look at the vertices.

07:20 Okay.

07:21 Here's the second part of your question.

07:24 Let's see.

07:25 So it starts at b, so it starts here, so it starts here at b and goes.

07:33 And i do have all the choices for this one.

07:36 Okay, it says, describe the relationship between the number of faces of an end -gone prism and of an engon pyramid okay so we got to do the same thing same idea so in a pyramid now let's make a let's do a hexagon does i ever do a hexagonal no i don't want to do that one let's do uh let's try the pentagon for a base um these are dotted so there's our base and they're all going to go to a point like that they all go to some one point.

08:24 That's dotted.

08:28 There you go.

08:29 Okay, so the faces are the flat sides.

08:32 Okay.

08:34 So all of the red triangles that go up to the point, there's one face for every single side of the base.

08:42 So for faces of a pyramid, there's one, two, three, four, five, there's one for every side of the base.

08:54 So again, there's a face for every side plus one.

08:59 For the bottom, for the base of the thing.

09:03 Okay.

09:06 In a prism, let's do, let's make it easy on myself.

09:13 I'll just do a, you know, a square.

09:17 Let's make the bases red.