Areas of Parallelograms - Free Educational videos for Students in K-12

Areas of Parallelograms - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:01	today we're going to talk about the area of a
00:04	parallelogram . Let's get started . Yeah . Alright .
00:25	Before we talk about how to find the area of
00:27	parallelogram . Let's back up a little bit . Well
00:30	, first , what are parallel grams ? Well ,
00:33	the quadrilateral . What are quadrilateral ? They're polygons .
00:36	So let's start there . What are polygons ? Well
00:40	, these are all examples of polygons . These are
00:44	not . What's the difference ? Well , the Pavilion
00:47	is a close figure in a plane made up of
00:51	three or more line segments . Now let's break that
00:55	down . First closed . That is closed . But
01:00	if I do the same and I stopped there ,
01:05	this little opening here means it is not closed and
01:07	therefore not at polygon . Next it is in a
01:10	plane . What does that mean ? We're not talking
01:12	about like an airplane . What we're talking about is
01:15	it's two dimensional . Okay , it's a two dimensional
01:18	figure , not three dimensional . And lastly it is
01:21	made up of three or more line segments that intersect
01:23	at their end point . Now what that means is
01:27	well if you ever try to make a polygon with
01:31	only two sides it's really difficult . It's always gonna
01:37	be open . It's impossible . So you've gotta have
01:39	at least three and they have to end at their
01:43	endpoints . So if I did something like this one
01:46	two three these do not intersect at their end point
01:52	. This is an end point and that is an
01:54	endpoint and they do not intersect at those endpoints .
01:58	So that is not a polygon . All right .
02:00	Now that we remember the basics of polygons , let's
02:03	talk about the different types . Well we have polygons
02:07	with three sides triangles . We've got polygons with four
02:10	sides quadra laterals , five sides , pentagon , six
02:13	sides , hexagons and so on . Let's focus on
02:16	just the quadrilateral . And if we look at the
02:18	quadra laterals there's a lot of different kinds but there's
02:22	some that have special names because they are special .
02:25	We've got trapezoid , we've got kites and then we've
02:29	got parallelogram . And if you look for parallelogram is
02:33	there are different kinds of parallelogram . We're going to
02:36	focus on parallelogram in general . Okay . Especially with
02:41	how to find the area of them . So first
02:43	what exactly is a parallelogram ? It's a quadrilateral that
02:47	has two pairs of parallel sides . Those sides .
02:51	The opposite sides also are the same length . Now
02:54	let's talk about how to find the area of a
02:56	parallelogram . And to start we're gonna start with rectangle
03:00	rectangle czar parallelogram but we want to know how to
03:04	find the area of a parallelogram . That is not
03:08	a rectangle . So if it looks a little bit
03:10	different . So what we can do is start with
03:14	a rectangle and we know how to find the area
03:16	of a rectangle length times width . You've done it
03:18	since probably 4th or 5th grade . But what if
03:21	it looks different ? What if we cut off a
03:24	triangle from that rectangle with a little chop now that
03:29	we've got a rectangle um and actually a trapezoid ,
03:34	if I move that rectangle , wow and those right
03:41	angles line up on the other side and we put
03:44	it together , this is a parallelogram . Did we
03:49	change the area from the rectangle that we had before
03:53	? And the answer is no it still covers the
03:56	same amount of space . The area is exactly the
03:59	same . We just moved some of it from one
04:03	part to the other . So now let's talk about
04:06	how to actually find the area of that . So
04:08	here we go . The area of a parallelogram .
04:11	It's just a product of its base and its height
04:16	and we know product means multiplication . So area of
04:20	a parallelogram is equal to base times height . Okay
04:24	. Now notice we don't use lengthen with And there's
04:27	a reason for that . Okay . one is if
04:32	you look at this and I ask you , well
04:34	, what's the length and the width you would say
04:35	? Well , okay , well maybe this we could
04:38	call the width . Is this the length or is
04:43	that a length ? And you get confused ? Okay
04:46	. Because it doesn't have right angles . We use
04:48	base and height in the key is the base ?
04:54	Oftentimes you think of it as the bottom , right
04:56	? But it doesn't have to be I could rotate
04:59	this up and it could look like that and this
05:07	could be the base . Okay . It doesn't matter
05:10	basis . Could could be different lengths depending on how
05:14	the shape is um written . Okay , but for
05:18	here that's gonna be my base and my height .
05:22	This is the key . The height has to be
05:25	perpendicular to the base which means it needs to form
05:28	a right angle . So this is not my height
05:32	. Okay That is my height . And it makes
05:36	sense right ? If we think of ourselves , if
05:39	I go to the doctor and they're gonna measure my
05:41	height , they don't take a ruler or not a
05:45	ruler but a tape measure and measure from over there
05:49	diagonally up to the top of my head . They
05:53	make me stand straight and they measure perpendicular with the
05:57	ground straight up . That would be your height .
06:00	It would be great if they measured it from over
06:02	there because I'd be a lot taller . But that's
06:05	not how they do it . So here if this
06:08	was my base , my height would be right there
06:12	. And that's how you find the area of a
06:14	parallelogram . Alright , example one find the area of
06:17	each parallelogram . So what we're looking for is the
06:20	base times the height . And remember basin height have
06:23	to be Perpendicular . So if I look here ,
06:27	I've got this 11 m over here , but notice
06:30	I don't have any length that's perpendicular to it .
06:35	So this is just here to mess with you .
06:38	It's just here to trick . You don't fall for
06:40	10 m and 12 m . Those are perpendicular .
06:43	So 10 m is my base perpendicular to that straight
06:48	up is 12 m my height . So for area
06:53	very simple 10 times 12 which is 120 . And
06:59	remember this is area . So the units have to
07:01	be squared . So 100 and 20 m squared .
07:06	Box . Man , that's like to be um Same
07:09	thing , We've got three different lengths here . Um
07:11	But not all of them are gonna have a perpendicular
07:15	relationship . So if I look at this and I
07:18	think well what's my base ? Nothing is really on
07:21	the bottom , we gotta point here . But that's
07:23	okay . You can rearrange it however you want .
07:26	So if I say , well what if I just
07:28	rotated it down here and this 6.5 was on the
07:32	bottom was my base ? Well then my height would
07:36	be going perpendicular to that . Well , that's great
07:40	. Here it is four ft , this That angle
07:44	right there is not 90°. . So this again ,
07:47	is there just to mess with you is just to
07:49	trick you . So here we go . Area is
07:53	base times height . The base we're gonna say a
07:57	6.5 ft Times my height , which is four .
08:03	And I can use the distributive property if I want
08:06	four times six is 24 plus a half times four
08:13	is too , Which gives me 26 units its feet
08:19	, but it's area so I'm gonna have feet squared
08:23	. And Fox my answer . Here's some to try
08:27	on your own . Okay , here's the last example
08:34	. Find the area of the shaded region . So
08:37	if we look here , I've got a parallelogram and
08:41	you may notice a few new markings on here .
08:45	You see these little arrows on the sides . Now
08:48	, what that means is the arrows decides that had
08:52	the same arrows . So these both have one those
08:55	little arrows on there , that means they are parallel
08:59	with each other . You know if these ones have
09:02	to and that's because they are parallel with each other
09:05	. They're showing that those lines are parallel or those
09:08	lines segments are parallel with each other . Anyway ,
09:11	so let's get back to the problem . So we've
09:13	got a parallelogram , but then we've got this cut
09:16	out here , um and it's 10 by 10 .
09:18	So this cutout square , we want to find just
09:21	the area of the shaded part that's in blue .
09:24	So what do we do ? Well , when you
09:26	think of something that's cut out , that should probably
09:29	make you think of subtraction . What if we had
09:32	the area of the entire parallelogram ? And then we
09:36	cut out or subtracted the area of that square ?
09:41	What's left ? Just the area of the shaded region
09:44	. So that's what we're gonna do . So ,
09:47	area of the entire parallelogram again , base times height
09:52	. Here is my base 16ft perpendicular right here Is
09:57	the height . So I've got 16 times 20 .
10:03	This represents the area of my entire parallelogram . And
10:07	I'm gonna subtract the cut up Which is the area
10:12	of that square , which is 10 times 10 .
10:16	And now let's just simplify . So 16 times 23
10:22	20-100 will leave me with 220 and the units here
10:28	are gonna be square feet or feet square . That
10:33	is the area of the shaded region . Here's one
10:37	to try on your own as always . Thank you
10:41	so much for watching , and if you like this
10:42	video , please subscribe . Mm .

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