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.