What I like is that I've been out of school for... (counts on fingers...) 43 years now and I can follow Eddie Woo without feeling like I need to start watching his videos from the very first one just in order to understand what he's talking about. An exemplary teacher!
You have been a lifesaver to at least one parent suddenly thrown into the deep end of trying to recall all this to assist a child trying to remote-learn during COVID-19 iso! Thank you!
Mr. Woo is a very gifted individual and teacher. Any of his students, present and former, who have gone on to college and taken higher level mathematics will realize what a remarkable and unique teacher he is. Incredible insight into explaining and communicating the essence, understanding and solution of the problems. Please appreciate this man and his enthusiasm and love of teaching. Thank you Mr. Woo for your teaching videos. They are engaging, educational and entertaining to watch and learn.
I think of the 1/2 (a+b) as the average of a and b, making a rectangle of equal area whose top/bottom length is that average and the vertical length as h.
For the Trapezium I looked at it like a rectangle constructed from b & h. Chopping it up into 3 sections, I was left with the middle of a*h and two ends that when added together create a rectangle of (b-a)*h. Now that a*h section, I put to the side momentarily as that is the actual area needed. As for the (b-a)*h, coming from the two rectangle sections made up of triangle pieces, they can be joined together in a fashion similar to the green portion of the Triangle example on the board. These are two triangles of equal heights, joined at the tip of their bases, thus 1/2 of a rectangle and as such, come to the formula for the section of ((b-a)*h)/2. Add this last portion of the formula to the earlier portion and you get (a*h) + (((b-a)*h)/2), a complete trapezium formula. After a bit of rearranging and Desmos testing, both this formula and the one shown give the same results.
I learned it by making another identical trapezoid, inverting it and making a parallelogram. Then the area of the parallelogram was (a+b)h. Divide by 2 to get the original trapezoid, therefore, (a+b)h/2.
A similar idea is to split it horizontally in half, then rotate the top half so it's inverted and then paste it on the right side. You're left with a parallelogram with base a+b and height h/2.
Hello Eddie, i'm from Brazil and you are inspiring me to become a teacher. I'm finishing my master's degree and i hope to become as good as you! Thank you!!!
Student asks for formula Eddie Woo: Its more important to know where the formula comes from than what is it. (I can't recall what he egg-zact-ly said, but it was something like that)
That's a cute question at 11:33 . I love it when children get to understand the beauty of math. Math is everywhere. It's just the way it's being taught.
I immediately thought of a*h + (b-a)*h, essentially cut a rectangle out of the center and glued the two remaining pieces together into one triangle. This method is far simpler though, and I will echo everyone's sentiment about wishing I had you as a math teacher when I was a boy.
I am 31. I have never seen this that way - I want to re-learn math with your channel. I will keep going through as many videos as I can to be a good support for my child in math! Awesome logic :)
I love the way you explain why you get to the formula. You might also add what seems obvious; that you just have a rectangle formula but as two of the sides are different, you have to use the average.
you can also think of (a+b)/2 as the average width of the trapezium. since the “error” / deviation from this width cancels out between the top and bottom halves of the shape, the area is the same as that of a rectangle whose width is (a+b)/2 - or h(a+b)/2.
Wow! Wonderful! I really loved how you made your class engaging by challenging your students. I remained hooked onto the video the entire time. Thank you so much for posting this.
One could say that the area formula for the square is still just base x height, but it just so happens base = height and thus reduces to s^2. Interestingly enough, the area of a square can also be calculated as 1/2(d^2), where d is the length of the diameter. But that DOES NOT work for all rectangles in general. (An easy way to see this is to imagine a 3 x 4 rectangle having area 12. The diagonal would be 5 forming two 3-4-5 triangles within the rectangle, but 1/2(d^2) would equal 12.5.)
Beautifully done! I tutor and am constantly trying to un-teach the tendency to memorise formulas... it's a losing game! Understanding the derivative nature of these formulas is SO much easier for students...
I've got another approach: 1.- duplicate de given trapezium and rotate it by 180deg in the plane. 2.-move it until one of its laterall side becomes coincident with the analogous side of the first figure. So you get a parallelogram of area to be equal to double of the initial trapezium. Considering that any base of this last figure is the sum of each bases (a and b) its area would be a+b*h then the half of this is the area we are looking for. I think that drawing this process on a blackboard becomes easier to understand becouse is shorter and doesn't require to divide by triangles. hope to bu helpfull. thank you.
Thank you ... thank you very much man you have helped me a lot, I love logic but didn't understand what they taught in school and now with your videos I can just feel complete,so thank you very much
You can visualize that geometrically, if you draw a rectangle with Base = a+b and heigth = h/2 overlapping with the trapezium, and then show how the uper parts of the trapezium, fit into the long rectangle.
Personally I always found learning more effective and worthwhile when the teacher only provided us with the minimal basics (Only how to work out a square for example in this case), and then introduced us to a problem we would have to figure out independently or in groups. I don't know if it's allowed, but if i were a teacher in my school (where teachers can teach however they see fit), i would make a poll to see who prefers which method (out of many) of learning. From what I saw and experienced, a lot of time is wasted for many students simply by the teacher not choosing a suitable teaching method for each specific class. There was a point when English started being exponentially more difficult for everyone in my class as more topics were introduced, merely because the teacher ONLY demonstrated and talked. We never did any independant thinking, which usually forces people to become more involved in the lesson and as a result get people to think more and harder... and so on, you see where i'm going with this. This is especially ineffective if the subject is boring to an individual. Though it was just two of my classes, English and Maths, that had these visible issues, statistically speaking, these classes could have been merely anomalous/outliers, i still believe it is possible for more classes to be like this. My point being: as a teacher, I would make a poll for every class I teach. Because it would be better if i was adapting my teaching methods to the majority, But what do I know? I never been a teacher. But if it's a good way to help these kids succeed even further, then there's no reason to not do it. You're already a great teacher, but why stop at greatness? (Unless you don't get paid enough so fair point haha) edit: note that i'm speaking in general. Some teachers alternate between teaching methods. Which i guess isn't a bad thing to do universally, but i don't know if it is still the best thing to do for specific classes, since i'm not a teacher.
@@AugustinSteven nah personally it's not for me. Besides, i'm already heading in a completely different direction. Also, quite literally. I was on a plane so nothing better to do.
I was teaching and came to this question where i needed to use area of trapezium, i didnt know it. So I used basic area sense which is base times hight, but there are two bases so I averaged them which is a+b over 2. That was a genius me feeling.
I turned on this video to see if your proof of the pattern for the trapezoidal area would be similar to mine, It's not. When I need to proof it I just draw similar trapezium at right side of first one. It create a parallelogram, and we can quickly deduce the area of the resulting figure. Our trapezium is a half of this figure. This is how the formula [(a + b) h] / 2 is obtained.
My suggestion: Produce each base to the right (or left) until they both measure a+b. Join the ends. Now you have a rhomboid that is twice the original trapezium. QED.
I was removed from high school cause I was too much of an idiot... here I am 17 years later watching a math video thats both interesting and confusing at the same time have no clue how to work out the area of a trapeze or whatever it is cause there was only letters in the answers??? Thank God I became a welder cause this shit would never sink in my thick head
Did you know a circle is a polygon? No, really it is. It's all about perspective. A circle is a polygon having an infinite number of infinitesimally small equally sized sides and an infinite number of angles each of which is infinitesimally close to 180 degrees. And a triangle is nothing but a trapez having a top base of length 0. Conversely, a trapez is nothing but a triangle with a top base greater than 0. A rectangle is also a trapez with the top and bottom bases being equal in length. A triangle is also a quadrilateral. It's a quadrilateral having one pair of adjacent sides separated by an angle of 180 degrees.
Thanks sir for your great information about maths . I am school student your maths videos helps me a lot for my maths and make me clear. keep doing your videos I will support you and share with my friends also. because youtube is not only for entertainment also for learning new things.
If you put another line h at the other end of a, you'd have 2 triangles and a square or rectangle to work with. Is that an invalid approach? Because I recall points reduction for doing it the way that worked best for my understanding.
2nd year mechanical engineering major... watching for fun, something about the videos are nice to binge watch.
Exactly. I am a master of science and love his videos - including this.
Late to the party but glad I'm not the only one watching for the fun of it
Why didn't I have a teacher like you 50 years ago in school? Brilliant work Eddie!
@@bojohannesen4352 lol
What I like is that I've been out of school for... (counts on fingers...) 43 years now and I can follow Eddie Woo without feeling like I need to start watching his videos from the very first one just in order to understand what he's talking about. An exemplary teacher!
That's the freaking right way to teach damn it! I wish my teachers are the same. Love ur lessons
You have been a lifesaver to at least one parent suddenly thrown into the deep end of trying to recall all this to assist a child trying to remote-learn during COVID-19 iso! Thank you!
Colin Chick
What is iso
@@evan.5967 isolation. Stay-At-Home order.
@@dmproductions9484
Oh...
Colloquialism these days...
These kids came up with an abbreviation that quick?!
lol
I’m not even in high school anymore and I still watch his videos sometimes 😂😂
Ime too but all the time
LEL LOL
@Bob Bob xd
Bob Bob BOB BOB
i havent been to highschool yet and im learning this😭
If I become a teacher I want to have just as good examples as you. Good video
*i f*
@@evan.5967 fuck the shut up
@@amalldekan1432 stfu
This argument is heating up, OH MY GOOOOD
@@amalldekan1432 who hurt u
Me *Sees an Eddie woo video that doesn’t have a complicated title*
Also me: It’s like I was made for this
Don't leave me hanging then, how do we chop it up to get the other two shapes.
@@TomekBlacksMyth elaborate what you're asking. Maybe I can help
also YOU: I'm a drama queen for numbers. 🙄
Mr. Woo is a very gifted individual and teacher. Any of his students, present and former, who have gone on to college and taken higher level mathematics will realize what a remarkable and unique teacher he is. Incredible insight into explaining and communicating the essence, understanding and solution of the problems. Please appreciate this man and his enthusiasm and love of teaching. Thank you Mr. Woo for your teaching videos. They are engaging, educational and entertaining to watch and learn.
Eddie: "More important than what the formula is, is where it comes from"
Me: My life has been a lie.....
I think of the 1/2 (a+b) as the average of a and b, making a rectangle of equal area whose top/bottom length is that average and the vertical length as h.
Steve Augustin same!
Aka. Average of bases times high.
Me too !
Same!
I ususally think of the bigger triangle it forms as it extends minus the little triangle.
For the Trapezium I looked at it like a rectangle constructed from b & h. Chopping it up into 3 sections, I was left with the middle of a*h and two ends that when added together create a rectangle of (b-a)*h. Now that a*h section, I put to the side momentarily as that is the actual area needed.
As for the (b-a)*h, coming from the two rectangle sections made up of triangle pieces, they can be joined together in a fashion similar to the green portion of the Triangle example on the board. These are two triangles of equal heights, joined at the tip of their bases, thus 1/2 of a rectangle and as such, come to the formula for the section of ((b-a)*h)/2.
Add this last portion of the formula to the earlier portion and you get (a*h) + (((b-a)*h)/2), a complete trapezium formula.
After a bit of rearranging and Desmos testing, both this formula and the one shown give the same results.
5:50 you can hear a "meow", odd
I learned it by making another identical trapezoid, inverting it and making a parallelogram. Then the area of the parallelogram was (a+b)h. Divide by 2 to get the original trapezoid, therefore, (a+b)h/2.
Really neat idea!
Cool!
I like this idea 💡😀
A similar idea is to split it horizontally in half, then rotate the top half so it's inverted and then paste it on the right side. You're left with a parallelogram with base a+b and height h/2.
Hello Eddie, i'm from Brazil and you are inspiring me to become a teacher. I'm finishing my master's degree and i hope to become as good as you! Thank you!!!
Student asks for formula
Eddie Woo: Its more important to know where the formula comes from than what is it.
(I can't recall what he egg-zact-ly said, but it was something like that)
Sir love you too much and I am from India you teach in easy language. That's why I like this video...
That's a cute question at 11:33 . I love it when children get to understand the beauty of math. Math is everywhere. It's just the way it's being taught.
Subscribed squared!…wish all teachers were like you…many thanks
I always teach the area of trabizum like you. Math is a peace of cake.... Mr.Mustafa Math teacher
bh + (h(b-a)/2) is also a formula you can use. Great video!
I immediately thought of a*h + (b-a)*h, essentially cut a rectangle out of the center and glued the two remaining pieces together into one triangle. This method is far simpler though, and I will echo everyone's sentiment about wishing I had you as a math teacher when I was a boy.
I am 31. I have never seen this that way - I want to re-learn math with your channel. I will keep going through as many videos as I can to be a good support for my child in math! Awesome logic :)
"more important than what the formula is, is where it comes from" 7:08. This is what was missing when I went to school.
Your an AMAZING TEACHER!! IM SO JEALOUS YOUR NOT MY TEACHER AT SCHOOL BUT I CAN STILL LEARN FROM YOU ON RUclips THANKS AND KEEP UP THE FABULOUS WORK
Wow what an amazing teaching skills you are talented teacher keep it up
I love the way you explain why you get to the formula. You might also add what seems obvious; that you just have a rectangle formula but as two of the sides are different, you have to use the average.
Best Math teacher ever!
mate i’ve got a maths test tomorrow and this is a life saver for revision
Great way to teach this lesson!! Nicejob
FANTASTIC Teacher!
you can also think of (a+b)/2 as the average width of the trapezium. since the “error” / deviation from this width cancels out between the top and bottom halves of the shape, the area is the same as that of a rectangle whose width is (a+b)/2 - or h(a+b)/2.
Wow! Wonderful! I really loved how you made your class engaging by challenging your students. I remained hooked onto the video the entire time. Thank you so much for posting this.
I wish i had a teacher like him in college!
One could say that the area formula for the square is still just base x height, but it just so happens base = height and thus reduces to s^2.
Interestingly enough, the area of a square can also be calculated as 1/2(d^2), where d is the length of the diameter. But that DOES NOT work for all rectangles in general. (An easy way to see this is to imagine a 3 x 4 rectangle having area 12. The diagonal would be 5 forming two 3-4-5 triangles within the rectangle, but 1/2(d^2) would equal 12.5.)
I can't find words to thank you enough, you're really a blessing!
i understood that very easily, those students are very lucky to have you as they're teacher.
i watch your videos to remind myself why i love maths
He never fails to teach something that’s actually interesting!!
I wish i had u as my math teacher back in high school so that i wouldn't think and cry thinking i was am idiot!
7:08 "more important than what the formula is, is where it comes from" 👍👍
Beautifully done! I tutor and am constantly trying to un-teach the tendency to memorise formulas... it's a losing game! Understanding the derivative nature of these formulas is SO much easier for students...
I wish I had a teacher like you!
I wish i could have interesting teacher like you in my school.
keep it up bro .. watching u from morroco :-)
Nice proof! I hadn't seen this one before.
MTSPP i thought this was the only proof?
Im currently studying for my masters to become a teacher, your videos are so exciting to me
Great video, easy to understand, fully grabbed my attention.
Such great teaching ! Great way of explaining things!
I've got another approach: 1.- duplicate de given trapezium and rotate it by 180deg in the plane. 2.-move it until one of its laterall side becomes coincident with the analogous side of the first figure. So you get a parallelogram of area to be equal to double of the initial trapezium. Considering that any base of this last figure is the sum of each bases (a and b) its area would be a+b*h then the half of this is the area we are looking for. I think that drawing this process on a blackboard becomes easier to understand becouse is shorter and doesn't require to divide by triangles. hope to bu helpfull. thank you.
Wow wonderful resolution of eddie's beauifulness///
Great teacher
Wonderful way of showing how all of the formulas are related. Well done sir.
🙋🏽
If you have such a great teacher then who needs a tution!!!!!!!🤩🤩
7:08
EVERYONE MUST PAY ATTENTION TO THIS LINE!
students need to be taught this
I fell in love with math thanks to Eddie
His video in the morning is a treat!!
Thank you ... thank you very much man you have helped me a lot, I love logic but didn't understand what they taught in school and now with your videos I can just feel complete,so thank you very much
Isn't it easier to interpret the formulas as the AVERAGE of the parallel sides multiplied by h. Because that's what (a+b)/2 in this case represents.
Teachers so often neglect explanations. We always have to show our working but were never shown how this shit works.
Edit: Until this dude rocks up.
S(k+1)(k+1)=trapezium
S- the smallest triangle in trapezium
k - scale between the biggest triangle and the smallest because they are similar
You can visualize that geometrically, if you draw a rectangle with Base = a+b and heigth = h/2 overlapping with the trapezium, and then show how the uper parts of the trapezium, fit into the long rectangle.
Personally I always found learning more effective and worthwhile when the teacher only provided us with the minimal basics (Only how to work out a square for example in this case), and then introduced us to a problem we would have to figure out independently or in groups.
I don't know if it's allowed, but if i were a teacher in my school (where teachers can teach however they see fit), i would make a poll to see who prefers which method (out of many) of learning.
From what I saw and experienced, a lot of time is wasted for many students simply by the teacher not choosing a suitable teaching method for each specific class.
There was a point when English started being exponentially more difficult for everyone in my class as more topics were introduced, merely because the teacher ONLY demonstrated and talked. We never did any independant thinking, which usually forces people to become more involved in the lesson and as a result get people to think more and harder... and so on, you see where i'm going with this. This is especially ineffective if the subject is boring to an individual.
Though it was just two of my classes, English and Maths, that had these visible issues, statistically speaking, these classes could have been merely anomalous/outliers, i still believe it is possible for more classes to be like this.
My point being: as a teacher, I would make a poll for every class I teach. Because it would be better if i was adapting my teaching methods to the majority, But what do I know? I never been a teacher.
But if it's a good way to help these kids succeed even further, then there's no reason to not do it. You're already a great teacher, but why stop at greatness? (Unless you don't get paid enough so fair point haha)
edit: note that i'm speaking in general. Some teachers alternate between teaching methods. Which i guess isn't a bad thing to do universally, but i don't know if it is still the best thing to do for specific classes, since i'm not a teacher.
Sounds like you should become a teacher.
@@AugustinSteven nah personally it's not for me. Besides, i'm already heading in a completely different direction.
Also, quite literally. I was on a plane so nothing better to do.
Auzzies sure have a funny name for trapazoid
Jacob Schmidt the fuck is a trapadroid
@@priyadarshanpandey6532 it's a "trapezium"
this helped a lot to connect formulas and such.
I was teaching and came to this question where i needed to use area of trapezium, i didnt know it. So I used basic area sense which is base times hight, but there are two bases so I averaged them which is a+b over 2. That was a genius me feeling.
Nice explanation 👌👍
please also do circle and other shapes
Separating the trapezoid into triangles to explain the area is a really good idea
I turned on this video to see if your proof of the pattern for the trapezoidal area would be similar to mine, It's not.
When I need to proof it I just draw similar trapezium at right side of first one. It create a parallelogram, and we can quickly deduce the area of the resulting figure. Our trapezium is a half of this figure. This is how the formula [(a + b) h] / 2 is obtained.
The math teacher I wish I had.
Beautiful explanation n concepts cleared 👏
I never thought of that. Cool stuff.
Ah so it's h multiplied by the average of a and b... my intuition was right lol
That’s the way I figured also. The calculation ends up the same but I wish he would have explained it that way too.
this math group is so good. do you guys agree with me?
Someone is finally making math more interesting
3627 ( trapezium ) + 2701 ( triangular ) + 50 = 6,378
6,378*1,000 = 6,378,000 = R_earth in meters
My suggestion: Produce each base to the right (or left) until they both measure a+b. Join the ends. Now you have a rhomboid that is twice the original trapezium. QED.
Really good video
I like your class because, students study too.
Wonderful video. If it can be reduced to 8 mins , it will cut straight to the chase
but great job Eddie!!
Always explains everything well
i m 24 n i still watch him
Take 2 trapeziums, flip one upside-down. You have a rectangle. Divide in half for trapezium
I was removed from high school cause I was too much of an idiot... here I am 17 years later watching a math video thats both interesting and confusing at the same time have no clue how to work out the area of a trapeze or whatever it is cause there was only letters in the answers??? Thank God I became a welder cause this shit would never sink in my thick head
Did you know a circle is a polygon? No, really it is. It's all about perspective. A circle is a polygon having an infinite number of infinitesimally small equally sized sides and an infinite number of angles each of which is infinitesimally close to 180 degrees. And a triangle is nothing but a trapez having a top base of length 0. Conversely, a trapez is nothing but a triangle with a top base greater than 0. A rectangle is also a trapez with the top and bottom bases being equal in length. A triangle is also a quadrilateral. It's a quadrilateral having one pair of adjacent sides separated by an angle of 180 degrees.
Thanks sir for your great information about maths . I am school student your maths videos helps me a lot for my maths and make me clear. keep doing your videos I will support you and share with my friends also. because youtube is not only for entertainment also for learning new things.
there are differents formulas of certain shapes u use
In America, the trapezium and trapezoid bear each other's names.
excellent sir ,
I wish , I were the best teacher than u in age of 21 🙏🙏
If you put another line h at the other end of a, you'd have 2 triangles and a square or rectangle to work with.
Is that an invalid approach? Because I recall points reduction for doing it the way that worked best for my understanding.
so cool how all of the formulas relate to eachother
Yeah, and the square is also just a base times height, it's just they're the same thing there!
thanks, it's really helpful
Making learning at home so much easier
Great video!!!!
awesome dude
good video
At this point I need to you to come teach me in person! Thanks !