Math Antics - Perimeter - Free Educational videos for Students in K-12

Math Antics - Perimeter - By Mathantics

Transcript


00:03	Uh huh Hi , welcome to Math Antics . In
00:08	this lesson , we're going to learn about an important
00:10	concept in geometry called perimeter perimeter is just a fancy
00:15	math term . That means the distance or length around
00:18	the shape . But what exactly does the distance around
00:21	a shape mean ? Well , distance or length is
00:25	a one dimensional quantity that we can measure with units
00:28	like centimeters , inches or miles . That means that
00:31	perimeter is also a one dimensional quantity that we can
00:35	measure with units of length . For example the perimeter
00:38	of a shape when it be just 10 , but
00:41	it could be 10 cm or instead of being just
00:44	25 , it could be 25 miles . The units
00:47	are really important when you're talking about perimeter . Okay
00:52	, but what exactly do we mean by around a
00:54	shape ? It seems like there would be a lot
00:56	of different ways to go around the shape . Some
00:58	of them would be short and some of them would
01:00	be very long . Well , perimeter means the absolute
01:05	shortest distance possible around the shape . That would be
01:08	the distance you'd get if you trace the path exactly
01:11	around the border or edge of a shape , a
01:14	good way to see what perimeter is is to imagine
01:17	that you could walk right along the edge of a
01:19	shape like this five sided polygon . Imagine starting at
01:23	one of the polygons , vortices and then walking along
01:25	each side until you got all the way back to
01:28	the point that you started from the total distance you
01:31	traveled would be the perimeter of that shape . In
01:34	this case , if the length of each side of
01:37	the Polygon was 10 m , the total length you
01:40	would travel along all five . Science would add up
01:42	to 50 m . Like another good way to see
01:46	what perimeter is is to imagine that you could take
01:48	a shape like this square and break it at one
01:51	of its corners . Then you could unfold the shape
01:54	until it formed a straight line . The length of
01:57	that line is the perimeter of the shape . Doing
02:00	this helps you understand why perimeter is a one dimensional
02:03	quantity , even though it applies to two dimensional shapes
02:06	like this square , It's one dimensional because it's the
02:09	distance of the lines that go around the two dimensional
02:12	shape . Okay , so now that you know what
02:16	perimeter is , how do we measure or calculate it
02:19	for different geometric shapes ? Well that depends on the
02:22	shapes . Finding the perimeter of shapes that have curves
02:26	like circles or hearts or things like that can be
02:29	tricky . In fact , we'll wait and talk about
02:32	the perimeter of a circle in another video . In
02:34	this video , we're just going to focus on how
02:37	to find the perimeter of polygons . Since polygons are
02:40	made from only straight sides , it's easy to find
02:43	their perimeter . If you know the length of each
02:45	side . All you have to do is add them
02:47	up and the total length you wind up with is
02:50	the perimeter of the polygon . Mhm . Let's try
02:53	doing that with a few examples . So you see
02:54	how it works . The first polygon will try as
02:57	a triangle . This triangle has three sides that are
03:00	each a different length , three cm 4 cm and
03:04	five cm . Now to find the perimeter of the
03:08	triangle . All we have to do is add up
03:10	the length of those three sides , three plus four
03:13	plus five equals 12 . But don't forget , it's
03:17	not just 12 , it's 12cm . Always remember to
03:21	also put down the units of the Perimeter . Okay
03:24	, that was easy . Let's try another one .
03:27	This time , our polygon is a rectangle and you
03:29	can see that the shorter sides are each five m
03:32	long And the longer sites are each 10 m long
03:36	. So let's add them all up . We can
03:39	add up the sides in any order . We want
03:40	to as long as we don't forget any sides or
03:43	accidentally count any of them twice . And I think
03:46	I'll add up the two short sides first five plus
03:49	five equals 10 . Next I'll add up the two
03:52	longer sites , 10 plus 10 equals 20 . And
03:56	now if I add up those two answers , I'll
03:58	get the total for all four sides . 10 plus
04:01	20 equals 30 . So the perimeter of this rectangle
04:05	is 30 meters . You thought I was going to
04:08	forget my units , didn't you not this time .
04:12	Uh , here's another good example . This is a
04:15	six cited regular polygon . A regular polygon means that
04:19	all its sides are exactly the same length . And
04:22	that's good because this diagram only shows the length of
04:25	one side 4cm . But since the polygon is regular
04:29	, we know that all the other sides are also
04:32	four cm long . Now we could just add up
04:36	all the sides like we did before , but since
04:38	they're all the same we can use multiplication as a
04:41	shortcut . That's because multiplication is really just repeated addition
04:45	. All we have to do is multiply the number
04:47	of sides . Six by the length of the sides
04:50	. Four centimeters six times four equals 24 . So
04:54	that means the total perimeter must be 24 24 .
04:57	What centimeters ? That's better . And this formula works
05:03	for any regular polygon , no matter how many sides
05:05	there are . If the sides are all the same
05:08	length , you can just multiply the number of sides
05:11	by the side length and you have the perimeter .
05:14	Okay , let's try one more example , this polygon
05:18	also has six sides but it's not regular polygon .
05:21	The sides are different lengths and this one is really
05:23	tricky because they only show us the length of four
05:26	of the sides . The other two are missing .
05:28	So how can we figure them out ? Problems like
05:31	this come up all the time and math problems where
05:34	you aren't quite given all the information when you have
05:36	this kind of problem . The key is to use
05:39	what you do know to figure out what you don't
05:41	know . Here's what I mean . Look closely at
05:44	the two vertical sides that we do know the length
05:47	of four and 6" . Now imagine that those two
05:52	vertical sides could be moved straight across to the other
05:55	side , the side that we don't know the length
05:57	of . By doing that , you can see that
05:59	the missing length would just be the combination of the
06:02	two vertical length that we do know four and 6"
06:06	. And since four plus six equals 10 , The
06:09	missing vertical side must be 10 long . Notice that
06:13	we can do the same thing for the horizontal sides
06:15	that we do know if we imagine those moving down
06:18	to the side that we don't know , we see
06:20	that its length must be equal to the combination of
06:23	those two lengths . 10 inches plus five inches equals
06:26	15 inches . There we've used the lengths that we
06:30	did know to figure out the lengths that we didn't
06:32	know . And now that we know the length of
06:34	all the sides , we can just add them all
06:36	up to get the perimeter . Four plus five plus
06:40	six equals 15 . And then 15 plus 15 equals
06:44	30 . 30 plus 10 equals 40 . And last
06:49	of all , 40 plus 10 equals 50 . So
06:53	the sum of all the sides is 50 and that's
06:56	the perimeter of this shape . And that's the end
07:00	of this lesson . We've learned that perimeter is the
07:03	distance or length around a geometric shape and we've learned
07:06	how to calculate it for any polygon . You just
07:09	add up the length of all the sides and the
07:12	total length is the perimeter . Oh and don't forget
07:16	your units . Also don't forget that to get good
07:19	at Math . Takes practice . Thanks for watching Math
07:22	Antics and I'll see you next time . Learn more
07:26	at Math Antics dot com .

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