I did it the HARD way!

I prepared all of this and later realized there was a shortcut I missed. Can you spot the easier method?

[@JasonMoir]

Love the dramatic flipping of the triangles.

[@powerzx]

I don't.

[@Danymillion]

​​@@powerzxshut up

[@kenhaley4]

Yeah, the shortcut is to look at the face and realize the shaded area is the larger upper triangle's area (12x16)/2 minus the smaller upper triangle's area (6x8)/2. That's 72. Multiply by the depth 50, and you have the answer 3600. Nevertheless, your video was fun to watch! Thanks for the great content.

[@jmsaltzman]

YES, this was one of the easiest problems shown, I finished it fast. How exciting :)

[@JonnyBoi957]

That is probably why the title is I did it the hard way

[@z000ey]

Even shorter: the way to divide a triangle (in this case the whole triangle consisting of the named trapezoid and the small corner triangle) in 4 same triangles of 4 same areas is to connect all midpoints, and by seeing this you know that the trapezoid has exactly 3x the area of the small triangle. This works for ANY triangle. Thus: V=bxh=3x(8x6)/2*50=3600

[@pimespo]

We all made it to the end because of how exciting it was.

[@HasanKhater]

Like the fact that you’re solving very simple math problems, for some reason it’s very entertaining, plus it’s good for the brain and keeping logic alive.

[@9876oti]

the taming apart of the other prisms + the triangle flip TRULY made this one exciting. thanks!

[@oofboxer]

i love how he animated it also 3:03 is very cool

[@bebektoxic2136]

Didn't expect that lol.

[@KMills]

Your videos have opened up so many shortcuts and concepts for me with math, I'd love a video on triangle mid segments

[@RobG1729]

I not only made it to the end, but replayed the latter portion calculating h. A long video for this channel is a third the length or shorter compared to math videos elsewhere. I appreciate your method of explanation and brisk pace.

[@noam9997]

The really hard way.. simply should be the triangle section made from the top 2 pieces, minus the top piece. (((8+8)*(6+6))/2)*50 - (((8*6)/2)*50) = 16*12*25 - 48*25 = 4800 - 1200 = 3600

[@Siddhantshekhar01]

Yeah please make a another video on the mid segment of triangles. Im pretty hooked in!

[@camerongray7767]

People who mentally solved it while looking at the thumbnail 👇

[@SpanishGarbo]

I made it to the end, don't worry.

[@curtisdaniel9294]

I made it to the end AND understood all of your work. I particularly liked how you isolated all the parts of the original object. How exciting. [ I borrowed that phrase from a math geek on KZbin 🙄]. Seriously, Andy, great work....as always. 💙👍

[@Wilba6582]

If you pair the long unshaded trapezoids with the triangles, and pair the identical shaded/unshaded trapezoids, you can form a parallelogram where each pair is 1/3rd the total area, thus the shaded trapezoid is 1/6th the area of the 24x18 rectangle.

[@irmabecx4758]

Good on you for doing it the hard way. Good on me following along having a history of failing math. I'd love to see something about the middle of triangles. :)

[@mattiadeis7044]

I made into the end!! Anyway yea you should do a video explaning the midpoints of a triangle or just straight up math!!❤❤

[@johngriffith182]

Yes! I made it to the end to check if I got the same answer using the two triangles in the upper left of the face. How exciting.

[@nimamousavi3352]

when simple solutions doesn't satisfy your brain needs

[@robbiekavanagh2802]

Divide the box into a grid of nine 8x6 boxes, the diagonals halve these boxes, the shaded area is made of three halved boxes, then times the length gives answer (8x6)(3/2)(50) = 3600m^2

[@EchoFox77]

i’m proud of myself for remembering the 3-4-5 special triangles and figured out b1 and b2 so much faster. it’s only been like 15 years since i learned that in high school geometry lol

[@henrygoogle4949]

Wow was not expecting the flipping excitement. I made it to the end.

[@petersimon2619]

Blew my mind with the triangle rotation

[@DrewsOnFirst]

Andy's method is how you get the first 3 problems right and have no time remaining to finish the other 7 on the test before class ends. 😛

[@juanvaldo666]

Great video man. Thanks

[@vipcesh]

due to the uniformity of the slices, and the even number of slices, you can reorder the slices to have equal 1/3 volume (slices numbered from left to right): 1+4=2+5=3+6. since slice 2=5 your formula is slice 2 = (18*24*50/3)/2 or 3600

[@rowrow_]

Finding the height of the triangle was so brilliant

[@AndyMath]

It is one of my favorite logical paths. Two things are equal. Change your perspective on one of them. Learn something new.

[@jreese8284]

Ah, relativity! 4 minutes isn't "long" for YT; although it's a bit long for you. Love your work!

[@generaleditz1]

I always make it to the end, and if there one thing i learned from this channel, it's that there is always a right angled triangle hidden somewhere

[@jamesrocket5616]

Nice, I love problems involving prismoidal volume which is applicable in earthworks (excavation and backfilling of soil).

[@aj__stha]

Shortcut method would be subtracting the smaller traingular prism with the bigger triangular prism, but this was fun as well. Thank you

[@maddening6850]

The triangle area of a triangle is it's base times it's height divided by two, the shaded prism is the area of one triangle minus another. B*H/2 - b*h/2 where B=8+8 H=6+6 b=8 h=6 Once you've found the face area of the prism the length is 50.

[@kmjohnny]

I think I see the easy solution, but I'd be bad at proving it. It has to do something with the ratios on the side - like the corner triangle fits 3 times into the middle one, and 5 times into the larger one. Add them up, that 9 triangle where the middle one takes up 3 spaces, so that's 1/3. This is half the rectangle on the side, so I divide it by to to get 1/6. Calculate the whole area, divide by 6.

[@matianz]

thanks andy xoxo

[@DanielNRollins]

Exciting, as usual

[@roblowery3188]

Of course, we made to 4:20 minutes. I have never left one of your vids early. great content, definately helping me knock the cobwebs loose.

That's a nice one. But after you found the b1 and b2 I would use trigonometry instead. The angle of the top right corner of the rectangle is the same that the angle of the trapisoid right bottom angle. So, first the rectangle's angle: arctan(24/18) = 53,13° Now the h: h = 6 * sin(53,13) => 6 * 0,8 = 4,8 From now everything the same. I think this is a litle bit simplier.

[@angelaogara1219]

Exactly 4:20 minutes, nice

[@Beiconqueso02]

How exciting

[@KingTurnell]

I want the video about mid segmentes in triangles

[@bIeed]

You need to calculate the surface of that is facing us and multiple by 50m. And to do that you start by drawing the smallest rectangle than includes the surface we need. And it its a: (8+8)x(6+6)=192 Than you calculate half of it since the diameter is one of the surface sides: 192/2 = 96 Than you calculate that small triangle on the top left: (8x6)/2 = 24 You add the two triangles: 96+24= 120 Than you substracte the the surface of the two triangles from the rectangle: 192-120=72 Now, you multiply the surface by the depth: 72x50= 3600m³ Sorry, I hope it made sense. My main language isn't English, I also calculated all that in my head.

[@AlmightyFSM]

Can you know for sure that the top and bottom of the trapezoid are parallel? The clue just says "prism", but there's nothing in the original diagram to assert that the lines in the base of the shaded area are actually parallel. I don't know if the word "prism" guarantees that does it? e.g. I don't know whether you can just "move the lower labels to the top" (1:06) can you?

[@bartomiejzemsta2932]

What a great video 😊 wow 🤩

[@donvito1973]

No need for Pythagoras, it's a 3:4:5 triangle, and both triangles are similar with scale factor of 2.. I love the triangle area equivalence though, excellent trick for finding the height.

[@Rorablink]

The hard way indeed😂 I could never

[@yn_km]

Bro you must make A lot more of these videos

[@wubbybubby1276]

For the height of the trapezoid, u also coulda used the GMT theorems of similarity, immeadiately getting (h/6) = (8/10) as a proportion

[@ccdsah]

nice numbers, did it all in my head

[@360_swagburittos9]

Never thought about the flipping triangle

[@danpliska924]

hi andy. i made it to the end of the video. great visual effects.

[@Mixa_Lv]

Wow, that is a massive prism

[@greendruid33]

Very nice - made it to the end for sure. How come you chose to do all the math for Pythagorean theorem when you could have pointed out that both triangles followed the 3-4-5 rule?

[@txikitofandango]

Break up the base into 18 triangles of equal area. The shaded part is 3 out of 18, or 1/6 the base area. So the volume is (1/6)(18)(24)(50) which you can do in your head

[@vincent412l7]

How did we assume a rectangle with right angles, and parallel lines to make a trapezoid? (The spacing is not given for the top).

[@tortinwall]

I made it to the end, after I’d worked it out in my head based on subtracting one 3:4:5 triangle from a bigger one.

[@arthhaa]

Andy Math, please solve a OBMEP ( The Brazilian Mathematical Olympiad of Public Schools ) question to be more specific the 6th question of 2023 level 3 phase 1

[@umbra0rpng173]

No views in 20 seconds... People aren't getting excited over math 😢

[@max-dd4xj]

What pc program do you use for pulling out pieces of figures?

[@billiboi122]

He did it the HARD way!

[@okalov]

Area big triangle minus area little triangle multiplied by the length of the prism and you've got it

[@cowofthemonth]

Just teselate the larger triangle into 9 smaller similar triangle, 1-3-5, so 3 times the smallest triangle --> 24*3*50

[@TheTomTracey]

Nice video length

[@robertdoherty4539]

Video being 4 minutes and 20 seconds is absolutely not a mistake

[@fadil9171]

I want to do maths like u What are the topics and sub topics I need to learn Assume I know nothing and I'm complete beginner I want to be like u guide me please

[@user-kl1me4zs1s]

You did it but it was too lengthy you could also just subtract those triangles (the bigger triangle including shaded part and the small triangle)

[@kujmous]

I was not prepared for the flip.

[@mulangumundemba9962]

I thought he was going to mention the fact that the triangle form a 3-4-5 special right triangle instead of working out Pythagorean Theorem.

[@notonlyhuman6073]

“This is probably gonna be a long video” Me looking at the vid length: nice

[@mrshreykumarjain]

I just subtracted the area of the bigger prism with area of smaller prism. Calculation of hypotenuse is easy... In just 1 min I got 3600

[@the_god_masterpiece]

Nice 🙂

[@Logia_]

Guys he is getting stronger with each view, he is now able to interact with the math himself. :0

[@dod-do-or-dont]

I will assume that the shaded Area is 1/6 of whole. As we have equal fragments. One is smaler 2nd is average 3rd is the longest. So by averaging, we should have 1/6 of whole intersection field. And just multiply by length Xd, i was right, WHO would gues

[@prplzbr]

Hey, I solved one! I did it the easy way, but still, I'm taking the win.

[@Nomedecor]

i did it to the end

[@davidvidic]

The easy way to do this is: (16*12/2 - 8*6/2)*50 = 3600 (area of Triangle with shaded part - area of smaller unshaded triangle) * length

[@VK-1981]

S1=(3/18)*S S=24*18 S1=3*24=72 V1=72*50=3600

[@thatonedynamitecuber]

I really need mid segments its so confusing

[@KasperDahlTangen]

And the easy way: Face = triangle + parallellogram = 8*6/2 + 8*6 = 72 Volume = Face * Depth = 72 * 50 == 3600

[@brandongraham3509]

3-4-5 triangles!

[@RichardTapp1]

I made it to the end, waiting for you to abandon that method and just deal with the two 3 4 5 triangles on the end face ...

[@drakkondarkspell]

Made it to the end.

[@Peter_Riis_DK]

I can spot another way, but it doesn't really seem easier. Let's have it.

[@emanuellindstrom4003]

I made it to the end 😊

[@hellkr]

I made it to the end ;)

[@RubyPiec]

midsegment of triangle video!!!

[@picknikbasket]

How extending!

[@k3vi0]

I made it to the end.

[@maa3563]

Is there eaven an easier way?

[@aljawad]

👍🏼

[@izme1000]

Simplifying all the way to 4.8 was an unnecessary step. You had 24/5. In the formula you were dividing by 2 and multiplying by 5. Those 10s would cancel out. It's not always worth it to get all the way to decimal.

[@cbl8439]

i made it! it was fun

[@jamie8703]

What in the hell is the easy way to find the area of a trapezoid without knowing the height or base lengths lol

[@BoolianKazooka]

Find the area of the triangular prism that has the trapezoid, then subtract the triangular prism in the very corner.

[@jamie8703]

@@BoolianKazooka YOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I DIDJT EVEN SEE THAT

[@richieE714]

I made it to the end lol

[@AsifAli-ym2cq]

4:20 length video again😂

[@yepyepmusic]

I've made it to the end

[@blakewright575]

Made it to 420!

[@YEOHWILSONMoe]

4.20 minutes noice

[@floweryfelix5190]

Actually it's called a cuboid

[@rodrigo53]

My guy… subtract

[@farmcat3198]

End

[@deniseockey6204]

What is the easy way if you solved it the difficult way?

[@Tiagovsk]

i did