Area of Triangle - Free Educational videos for Students in K-12

Area of Triangle - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Math channel . This
00:01	is a quick video looking at how to work out
00:03	the area inside a triangle . That is one of
00:05	these nice two dimensional shapes with three sides here .
00:08	It's important before we start , I guess , to
00:10	work out how we describe area what sort of units
00:14	we use because it's a two dimensional shape . Because
00:16	can't use standard distance units , we have to use
00:18	a special type of unit one that describes two dimensions
00:22	. Okay , two dimensional shapes . So rather than
00:25	just having one m , we actually have a meter
00:27	by a meter measurement which is used , which is
00:29	called say a meter squared . This could also go
00:32	for inches squared , an inch by an inch or
00:34	mile square mile by mile . But we actually use
00:37	these square units to describe the amount of square space
00:41	inside here . Okay , the amount of space inside
00:43	here . So let's just launch into a few examples
00:46	. So the example I have here is we have
00:49	a triangle that has a side length we could say
00:51	is three m . A side length of four m
00:55	and a side length of five m to work at
00:58	the area of a triangle . I'm just going to
00:59	show you how a formula is derived . We will
01:02	give you a formula , but I'm just going to
01:03	show you how we've got that formula . You can
01:05	see this triangle here , we can extend this triangle
01:08	out and so we can make it into a rectangle
01:11	. Okay , so we could have a side that's
01:12	parallel to hear that comes out three and a side
01:15	that also comes out four . That goes over here
01:17	, and you can see what we have here is
01:19	what we end up with . Is we end up
01:21	with a rectangular shape . Okay , how would you
01:23	go about working at the area of a rectangle ?
01:25	That's pretty simple . You would go , the area
01:27	is equal to the length times the width and that
01:31	would be nice and easy . We would say the
01:33	length is equal to four , we would say the
01:36	width is equal to three . And then we would
01:39	multiply through and go , okay , we have this
01:41	area of 12 m squared . But we have a
01:44	bit of a problem here because we are not dealing
01:47	with a rectangle , we're dealing with a triangle .
01:49	But pretty simple . Right ? Because what you'll notice
01:51	is this triangle is half the size of this rectangle
01:55	. So for all of this , what we really
01:56	just need to do is we need to just divide
01:58	our answer by two . Okay , so we divide
02:02	this part by two and then we get four times
02:04	three divided by two and our answer divided by two
02:08	. And what would end up with is the area
02:10	of our triangle , which is half the rectangle .
02:13	It's six m squared . So we can end up
02:15	with a formula which is a little bit are different
02:19	to the rectangle formula . And it's written as follows
02:22	, The area of a triangle is equal to the
02:24	base times the height Divided by two . And you're
02:28	going to see there's a bit of a difference here
02:30	why we use base and height instead of length .
02:32	And with and I'll show you this in a second
02:34	why this is important . But it's sort of the
02:36	same sort of thing . We have a base ,
02:38	we have a height and we're divided by two .
02:41	Okay , so pretty simple . But the reason we're
02:43	actually doing this is as follows , lengthened with well
02:47	, pretty much are we using base and high ?
02:49	What it actually tells us . We are going to
02:50	have to use a base here . And we use
02:52	the height from that base . The perpendicular goes straight
02:56	up . And we have this height here . We
02:58	could also use this base here as five . It
03:01	would be equally as valid . Where we would actually
03:03	use a high that would come off perpendicular like this
03:06	. And we could actually go base times height .
03:08	That would give us a similar sort of area .
03:11	And that's why we use this particular our formula .
03:14	Rather this length times width divided by two . Let's
03:16	have a look at a couple more examples . Okay
03:19	, this example . Here we go . We're trying
03:20	. It looks a little bit different . It has
03:22	a base of four centimeters and a height of 3.5
03:26	centimeters . So you could probably easily work out the
03:29	area in centimeters squared . But let's do that .
03:32	Okay , so the area is equal to the base
03:35	here , which is four centimeters . This is multiplied
03:38	by the height , which is 3.5 cm . And
03:43	this whole lot is divided by two . So what
03:46	do we have here ? Four centimeters by 3.5 centimeters
03:49	. Well that is equal to 14 centimeters squared .
03:53	Divided by two . Our answer . This is seven
03:55	centimetres squared . It's pretty simple . Right ? Working
03:58	at the area of a triangle is very , very
04:00	easy . This is one thing to watch out for
04:01	and you may want to be aware of this .
04:03	Say for instance , we have started this and I
04:05	said that we're not dealing with 3.5 centimeters . We
04:08	were dealing with 35 millimeters . It's important that if
04:11	you're working at the area of anything , you get
04:14	the units the same first . So we're trying to
04:15	work out our answer in centimeters squared , we would
04:18	change both of these two centimeters . We wouldn't just
04:20	go four cm times 35 mm because we would get
04:23	the wrong answer and we wouldn't have these standardized tends
04:26	to work with , we would have changes across the
04:28	3.5 cm first . Just watch out for that .
04:31	So let's just go through one other type of example
04:34	of a triangle that you might get . Okay for
04:36	the final example , we have this particular shape here
04:38	. It's a bit of a strange looking triangle .
04:40	It's an obtuse triangle . They look a little bit
04:42	different , but you work them out exactly the same
04:45	. You get the base , you multiply by the
04:47	height , you divide it by two . And the
04:49	reason this works is you can actually draw , you
04:52	draw a rectangle here . You can draw this line
04:54	that went parallel to this line here , and you
04:56	can draw this line which was parallel to this line
04:58	down here , and you'd end up with this particular
05:00	shape here , which is a parallelogram parallelogram . You're
05:04	working out by just going base times height . We're
05:07	working at half a parallelogram . So we're going to
05:08	go base times height divided by two . Right ?
05:11	So uh let's work it out . Pretty simple .
05:14	Okay , so the base here , this is in
05:16	inches and we're gonna be working this out in square
05:18	inches . So to work out the area here ,
05:20	we have the base which is two inches . Okay
05:23	, so two inches , this is going to be
05:25	multiplied by the height which is three inches And the
05:29	whole lot is going to be divided by two .
05:32	So two inches times three inches is six inches squared
05:36	. We're going to divide that by two . Our
05:39	answer six divided by two is three inches squared .
05:43	So that's how you work out the area of triangles
05:46	. If you like the video , please remember hit
05:48	the like button and comment if you want to make
05:50	a comment . Always welcome and I thank you for
05:52	watching . We'll see you next time . Bye .

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