Areas of Trapezoids - Free Educational videos for Students in K-12 | Lumos Learning

Areas of Trapezoids - Free Educational videos for Students in k-12


Areas of Trapezoids - By Anywhere Math



Transcript
00:0-1 Welcome to anywhere Math . I'm Jeff Jacobson . And
00:02 today we're gonna talk about how to find the areas
00:06 of trapezoid . Let's get started . All right .
00:27 Today , we're talking about how to find the areas
00:29 of trapezoid . Now , as a refresher , trapezoid
00:32 , Czar quadra laterals , which means they have four
00:35 sides . Uh and they have exactly one pair of
00:40 parallel sides . That's really important . Now , before
00:43 I show you what the formula is for how to
00:46 find the area of a trapezoid , let's look at
00:49 where the formula comes from . Okay , let's talk
00:53 about where the formula for the area of a trapezoid
00:56 came from because that's really important to know where it
00:58 came from . These formulas don't just appear out of
01:01 thin air , There's a reason behind it . And
01:04 if you understand where it came from , it gives
01:07 you a deeper understanding of how to find it and
01:09 hopefully you're not just concentrated on memorizing the formula because
01:13 memorizing stuff isn't any fun . It's much more interesting
01:16 to know where it came from . So here is
01:19 my trapezoid . Uh It's got four sides . It's
01:21 a quadrilateral like I said earlier . Uh and it
01:24 has exactly one pair of parallel sides . Uh These
01:28 little arrows here mean that this side and this side
01:32 are parallel with each other . So now let's label
01:34 um your parallel size , you're always gonna call those
01:38 bases . Uh and it doesn't matter which one you
01:41 label which but this top one I'm going to call
01:43 that be one for base number one and this bottom
01:46 for base number two . Remember your bases are always
01:50 gonna be those parallel sides . So it doesn't matter
01:53 if this is flipped up or rotated over wherever you're
01:57 parallel sides are . Those are going to be your
01:59 basis . And I could call this B . Two
02:01 and this one B . One , it doesn't really
02:02 matter then the distance between your basis right here is
02:07 going to be your height . Okay ? And same
02:10 thing , even if it's kind of uh kind of
02:13 rotated a little bit and might not look like a
02:15 typical height , the distance between your parallel sides will
02:20 be your height . Okay ? So look for that
02:23 , and it's always gonna be , your height is
02:25 always going to be perpendicular , Right ? That's what
02:27 that means to your basis . Now , now that
02:31 we have , my trap is always kind of labeled
02:34 . Let's look at where the formula came from .
02:37 If I draw a little line here from the mid
02:41 point on this side , all the way up to
02:42 here , and cut this little piece off and rotate
02:46 it and then slide it down . Well , now
02:50 I've made one big triangle . Ok ? And notice
02:55 the area didn't change , I still have the same
02:58 amount of red . Right , I just cut a
03:00 little piece off and moved it , that's all I
03:03 did rotate it and then moved it down . Um
03:06 So the area hasn't changed from my original trapezoid .
03:09 So now it's just a triangle . And to find
03:12 the area of a triangle , we know it's just
03:13 based on the height divided by two . Well ,
03:16 what is my base ? Well , my base is
03:18 just going to be my original B . One plus
03:22 my original B . Two . If I add those
03:25 together , that will be the base of this triangle
03:29 . The height is still this height . Okay ,
03:32 so to find the area of this triangle , I
03:35 would do B . one Plus B two times the
03:39 height and then divide all of that by two because
03:42 it's triangle . So with that in mind , here
03:46 are the formulas for area of a trapezoid . You
03:51 can even think of it this way right ? B
03:52 . One plus B two times that by the height
03:55 and then one half of that . Or you can
03:57 think of it as this way again . B .
03:59 One plus B . Two in parentheses , do that
04:01 first times your height , and then divide all that
04:04 by two . They're the same formula has just written
04:06 in different ways . So whichever one you're more comfortable
04:08 with uh Kind of concentrate on that . Lastly if
04:12 you're wondering . Well , does that work for any
04:14 trapezoid ? Yes , it will . Obviously , I'm
04:16 not going to show you all different trapezoid . Uh
04:19 But yes , believe me , it would work for
04:21 any trapezoid . Okay . Example one find the area
04:24 of this trapezoid . So if you remember what we
04:29 just found was the formula for area of a trapezoid
04:33 . Area of a trapezoid . Was the height of
04:36 the trapezoid times be one , whatever . The first
04:40 base plus B . To the other base , and
04:44 all of that Divided by two . Okay , so
04:48 let's look at our trapezoid . Uh it's pretty simple
04:52 . All we have to do is just start substituting
04:55 My height and my bases in here . Then simplify
04:58 . Okay so uh my height was if I looked
05:02 like I was six ft , So I'm gonna put
05:05 that there uh b . one , it doesn't really
05:08 matter which base you choose for B . One and
05:11 which one you choose for me to just remember your
05:12 basis have to be those sides that are parallel to
05:16 each other . Trapezoid has exactly one pair of parallel
05:21 sides . So I look for those parallel lines .
05:24 So let's say my B . One is five Plus
05:28 B . two then would be nine . All of
05:31 that divided by two . Okay so I'm gonna do
05:34 everything in the numerator first and then I'm gonna simplify
05:38 Uh now here I could be distributed property but I
05:42 can simplify these in the parentheses , so it becomes
05:45 six plus 14 Over two . And also if you're
05:52 comfortable with this , uh I could simplify here too
05:55 . I can say this becomes one , this becomes
05:58 three . So now it's just three times 14 which
06:02 is 42 . And now never forget your units .
06:09 These were in feet and its area . So my
06:12 units are feet square , 42 ft square . Okay
06:17 , if you didn't want to simplify here , you
06:19 could have done six times 14 and then divided by
06:22 two and you would have gotten 42 as well .
06:25 Okay , let's try another example . Okay , example
06:28 to again find the area of the trapezoid , we're
06:31 gonna use the same formula . But this time if
06:34 you notice this trapezoid is looking a little bit different
06:38 kind of on its side . Now you've got to
06:41 be careful when you , when you see trapezoid like
06:44 this , you have to identify what the bases are
06:48 and the basis might not necessarily be on the bottom
06:52 . That's okay . Just remember your basis . Have
06:55 to be parallel to each other . Okay , so
06:59 if I look here , those sides that are parallel
07:03 to each other are here on the on the left
07:06 side and then on the right side those are parallel
07:09 , which means those are my basis . So I'm
07:11 gonna leave the age for a second and let's say
07:14 B one then is eight millimeters plus B two then
07:18 would be four millimeters . Okay , Now now that
07:22 we have that are basis , we gotta look for
07:24 the height . The height is always going to be
07:27 perpendicular to the basis , right ? It's going to
07:30 form a right angle . So if you look here
07:33 the height then is this 5 mm ? Okay ,
07:36 that's got to be my height . So it's a
07:39 little different when they start kind of rotating the trapezoid
07:44 . They're trying to trick you a little bit .
07:45 Just be careful look for those parallel bases and then
07:49 a perpendicular height . Okay . And then all of
07:52 that . Don't forget divide by two . Okay ,
07:56 so now my area . Well five times 12 divided
08:03 by two . Again , I can simplify if I
08:05 want , but maybe I'll do it the other way
08:06 just so you guys can see uh five times 12
08:10 gives me 60 divided by two is 30 . Don't
08:14 forget your units . This is in millimeters squared .
08:18 You guys this area . Okay . Here's something to
08:21 try on your own as always . Thank you so
08:29 much for watching . And if you like this video
08:31 , please subscribe .
Summarizer

DESCRIPTION:

OVERVIEW:

Areas of Trapezoids is a free educational video by Anywhere Math.

This page not only allows students and teachers view Areas of Trapezoids videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.


GRADES:


STANDARDS:

Are you the Publisher?

EdSearch WebSearch