Surface Area of Prisms and Pyramids - Free Educational videos for Students in K-12

Surface Area of Prisms and Pyramids - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson and today
00:02	we're gonna talk about finding the surface area of prisms
00:05	and pyramids . Let's get started . Today , we're
00:26	gonna learn how to find the surface area of prisms
00:29	and pyramids and to do that . It's fairly simple
00:31	. All you do is find the some of the
00:34	areas of all the faces and that's it , that's
00:38	your surface area . You just add up the areas
00:41	of every individual face . Okay ? Um so let's
00:44	look at our first example and get started . Example
00:47	one . Let's find the surface area of this rectangular
00:51	prism . Now , to start off , I'm gonna
00:53	show you how to find the area the surface area
00:57	of this prism . Using a net and a net
01:00	is just a two D two dimensional representation of a
01:05	three D . Solid . That's all it is .
01:07	Okay , so basically you can think of , we're
01:09	gonna kind of cut this and like unfold it .
01:13	That's basically what you're doing to to make a net
01:16	fold down this back . I'm just gonna fold it
01:19	down so that will be like that . Okay well
01:23	then I've got I still have this very bottom that
01:26	that's going to be connected to . There's my bottom
01:31	. I'm gonna fold down this front , fold it
01:34	down . So this maybe I'll make a little note
01:36	. This was the back that was the bottom .
01:42	Now I'm gonna fall down the front . Yeah that's
01:48	going to be my front mm . Okay I'm gonna
01:52	fall down the side . Uh That's gonna be a
01:55	little bit skinnier . Another rectangle . There's that side
02:01	, I'm gonna do the same thing here on that
02:03	side and last but not least . And this is
02:10	the one thing that a lot of people forget when
02:14	they're making the net is the top and if you
02:17	remember that that's great . Uh you can either put
02:20	it on this side or this side . Kind of
02:22	like it folds all the way over . I'll just
02:24	go ahead , I'll put it over here . That's
02:26	gonna be the same size as the bottom . So
02:30	do your best . Obviously it's not going to be
02:33	perfect but that's okay . So that is the hop
02:37	okay . Um So there's my net but I'm missing
02:42	something . Hopefully you noticed that I don't have any
02:44	of my legs in there . So let's add that
02:47	uh this length here , It's the same as here
02:51	. Right then folded up . Or you can think
02:53	of the front folded up . That was the kind
02:55	of the height of my front and back . So
02:58	that's going to be here . So I'm gonna lay
03:00	without 3" . This is also 3" 3" 3" .
03:04	Right . Um Let's see what else . Well this
03:09	length here 4" , right , that's the same here
03:12	for 44 so maybe I'll just put it there .
03:15	That'd be easy . uh the length going back on
03:19	my side here with seven so that's here seven inches
03:23	seven inches seven inches . All of those going along
03:26	maybe I'll put it here seven inches okay . Um
03:30	And that's that's good enough . Right so with this
03:34	now hopefully it's making a little bit more sense in
03:38	looking a little bit easier on how to find the
03:42	area . Um Now that it's two D . Right
03:46	we just have a whole bunch of rectangles and we
03:49	know how to find the area of that . So
03:51	back in front kind of the key with this is
03:55	to be organized . Um So I'll just say mhm
04:01	. Back in front . Well Three times four is
04:06	12 but I've got two of them to back in
04:09	the front so that's going to give me 24 .
04:13	Uh Let's do this to swoop let's do the two
04:17	sides . Yeah , I've got these two sides here
04:22	, side . Inside . Well , uh that's gonna
04:25	be three , I'm sorry . Missing name . Yeah
04:30	, that's gonna be three . This is also three
04:32	. I'll just put that . There are three and
04:33	33 times seven is 21 times 22 sides . That
04:38	are the same . That can grow in 21 21
04:41	. It's got too many pens . Uh 42 .
04:46	Then I've got my top and bottom . Okay .
04:52	Uh The bottom four times seven . Well , give
04:58	me 28 . times two because there's top and bottom
05:01	, they're both can grow . It is 56 .
05:05	Okay . And remember surface area is just the sum
05:08	of all of the faces . So , my last
05:11	step , It's just to add all of those up
05:14	. Okay . And if I do that , let's
05:16	see . 56 and 24 is 60 , 80 Plus
05:22	. is 122 . So maybe All right . Let's
05:26	see how Put it up here . S.A . surface
05:29	area is 122 . And at the end I got
05:33	to remember my units inches , but it's area so
05:37	it's inches squared . Yeah . Mhm . For my
05:42	final answer . Okay . So that's how you find
05:46	the area . Sorry , the surface area of a
05:49	rectangular prison . Using a net . Okay . Here's
05:53	some to try on your own . Alright , example
06:02	to let's find the surface area of this triangular prism
06:05	. Um So , we're gonna do it using the
06:07	net again when you're making the nets . There's not
06:10	just one way to make the net . It all
06:13	depends on how you want to fold it out and
06:15	, you know , one way or the other .
06:17	It doesn't matter . Um So if you make your
06:20	net a little bit different than mine , that's okay
06:22	. As long as you're getting the same result ,
06:24	we got a bottom rectangle right there , that's the
06:28	bottom . Yeah , you can see that . And
06:34	really ? I think it helps a lot if you
06:36	label right , it can get very confusing . So
06:39	my suggestion is to label just like I'm doing here
06:42	. So this is gonna fold out and it's going
06:44	to look something like that , this is gonna fold
06:47	forward , It's going to look something like that .
06:50	Uh So that's gonna be the back , that's gonna
06:54	be the front . Uh Then we have this side
06:59	here um is kind of small . That's something like
07:06	that aside uh And then again the one that a
07:09	lot of people forget the top . I'm gonna fold
07:13	it the other way . Um And it should be
07:15	a lot longer than this , but I don't have
07:18	a lot of room . So just bear with me
07:21	that's gonna be the top . Now let's add Our
07:26	legs in there . So let's see uh here 12
07:30	cm uh eight cm here on this side . Eight
07:36	centimeters Five cm is here the height there five cm
07:41	. It's also here , even though it doesn't look
07:45	like it . My drawing mine , it's not perfect
07:48	. uh 13 cm along there . Okay , And
07:53	that's also five cm . That's also five cm ,
07:56	that's fine . Um let's see the top . Ah
08:00	we've got eight there . Um Let's see what else
08:04	. This length here is also 13 centimeters and I
08:09	mentioned that right , it's not it should be longer
08:12	but oh well okay so now I think we're ready
08:16	now here , it's not going to be quite as
08:18	simple as the prism because we don't have I mean
08:21	some of our shapes are doubled right the back in
08:24	the front of the same , But top bottom side
08:28	they're not the same . So you can't just multiply
08:30	it by three . So just be careful on that
08:33	. Uh Let's start with the back in the front
08:37	. Uh huh . Finding the area of a triangle
08:40	. Remember base times height divided by two . But
08:43	because I have two of them , I'm not going
08:46	to divide by two because I could divide it by
08:48	two and then do the same thing at them together
08:50	and have a whole . So I'm just gonna do
08:52	base times height and not divided by two . And
08:55	that will give me the two triangles . Uh so
08:58	that's gonna be let's see base time site 12 Times
09:03	five . Remember this is not the height of the
09:06	triangle , right height , the basin that I have
09:09	to be perpendicular . So 12 times five is 60
09:13	. Mhm . Yeah . Again , I could divide
09:15	by two and that would be 30 , but I've
09:17	got two of them , so 30 and 30 gives
09:19	me 60 again . So there's my front back .
09:23	Uh let's go with a sign . Uh five times
09:27	8 is 40 . That's simple . The bottom ,
09:33	The bottom is gonna be 12 times eight . That's
09:37	what , 96 . Uh and finally , the top
09:41	is going to be 13 times eight . See top
09:46	13 times eight . What's that gonna be 8104 .
09:53	104 . Yeah . Uh And finally , for surface
09:57	area , it's the sum of all of those faces
10:00	. So I'm gonna add them all up and my
10:04	surface area . Let's see . That's too 200 right
10:08	. 300 side 300 . uh and now I gotta
10:14	remember units , Centim , but it's areas to 300
10:19	cm squared . For my final answer . Here's some
10:25	more to try and you're up . Example three .
10:34	We have a square pyramid . We've already done a
10:37	couple of prisms . Now , let's move on to
10:39	pyramids . Same thing . Find the surface area .
10:42	Uh , let's make a net . So first thing
10:46	, it's a square pyramid . So my base is
10:48	a square . That's going to be simple . I'm
10:50	sorry , I'll get a different color . There's my
10:56	square . All the sides , you should know ,
11:00	all the sides of the pyramid are gonna be triangles
11:03	. Uh , so , and because it's a square
11:05	, they're all going to be the same . There
11:07	are gonna be congruent . So I'll have a triangle
11:10	there when I fall down that back , I'll have
11:13	a triangle on this side . When I fold that
11:16	one over triangle down here . When I fold the
11:20	front down and this side fold it over , will
11:24	give me a triangle there . Okay , now let's
11:28	add in some , some length . So That's going
11:31	to be seven m , 7 m , seven m
11:33	7 m . It's a square . Um now hear
11:36	this 10 m that notice it's on the it's on
11:42	the surface of the triangle itself . It's not inside
11:45	, it's not the height of the pyramid . Right
11:48	. The height would be coming from the base all
11:50	the way to that vertex at the top . Instead
11:53	, it's the height of the triangle here . It's
11:57	on this slant . It's called the slant height .
12:03	Okay . And when we start to do volume of
12:08	pyramids , then that's really important to know that compared
12:11	to the height of the pyramid . Um , but
12:13	we have that because we needed to find surface area
12:17	. So that is the height here . Of The
12:22	triangles , right ? The faces . Those triangles .
12:24	So that's gonna be what , 10 m . Okay
12:30	, So now we have everything , we need to
12:32	find the surface area . So let's go ahead .
12:34	Uh , I'll just start with the base . That's
12:38	the simplest . The base . Seven times . Remember
12:42	, this is a square . So I'll put a
12:44	seven there seven m . Seven times seven is 49
12:48	. So the area of my bases 49 . Um
12:52	Now the area of one of my triangles Would be
12:56	seven . The base times that height seven times 10
13:00	is 70 divided by two because it's a triangle ,
13:04	but we have four of them . So if you
13:09	think about it , this and this would be a
13:12	whole . That and that would be a whole .
13:14	So Instead of dividing by two . So here are
13:18	my I mean if you want you can find the
13:23	area of each one . I'm just kind of showing
13:24	you a shortcut . So when we call these the
13:27	sides , So that would be seven times 10 is
13:30	70 . Think Divided by two would be 35 .
13:36	But then I'd have to multiply it by four ,
13:39	Right ? Multiply by four with divide by two .
13:43	So that would be the same thing as just multiplying
13:46	that by two , which is 100 and 40 .
13:50	Okay . And if , if you're not following ,
13:53	uh , just do it the long way and you
13:55	should notice that will be 35 35 which is 70
13:58	35 35 70 70 and 70 is 1 40 .
14:03	Okay . Uh , and finally surface area , add
14:07	it all up . 1 40 plus 49 is 189
14:13	units will be meters squared . Yeah , here's an
14:19	example to try on your own . Thank you so
14:28	much for watching . And if you like this video
14:30	, please subscribe .

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