I prepared all of this and later realized there was a shortcut I missed. Can you spot the easier method?
Жүктеу.....
Пікірлер: 129
@JasonMoir16 күн бұрын
Love the dramatic flipping of the triangles.
@powerzx
16 күн бұрын
I don't.
@Danymillion
13 күн бұрын
@@powerzxshut up
@kenhaley416 күн бұрын
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
16 күн бұрын
YES, this was one of the easiest problems shown, I finished it fast. How exciting :)
@JonnyBoi957
16 күн бұрын
That is probably why the title is I did it the hard way
@z000ey
16 күн бұрын
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
@pimespo16 күн бұрын
We all made it to the end because of how exciting it was.
@oofboxer16 күн бұрын
i love how he animated it also 3:03 is very cool
@bebektoxic2136
16 күн бұрын
Didn't expect that lol.
@HasanKhater5 күн бұрын
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.
@camerongray776716 күн бұрын
People who mentally solved it while looking at the thumbnail 👇
@9876oti16 күн бұрын
the taming apart of the other prisms + the triangle flip TRULY made this one exciting. thanks!
@KMills16 күн бұрын
Your videos have opened up so many shortcuts and concepts for me with math, I'd love a video on triangle mid segments
@RobG172916 күн бұрын
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.
@SpanishGarbo16 күн бұрын
I made it to the end, don't worry.
@Siddhantshekhar0116 күн бұрын
Yeah please make a another video on the mid segment of triangles. Im pretty hooked in!
@noam999716 күн бұрын
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
@angelaogara121916 күн бұрын
Exactly 4:20 minutes, nice
@Beiconqueso02
16 күн бұрын
How exciting
@DrewsOnFirst16 күн бұрын
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. 😛
@curtisdaniel929416 күн бұрын
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 KZread 🙄]. Seriously, Andy, great work....as always. 💙👍
@johngriffith18216 күн бұрын
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.
@irmabecx475816 күн бұрын
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. :)
@petersimon261916 күн бұрын
Blew my mind with the triangle rotation
@mattiadeis704416 күн бұрын
I made into the end!! Anyway yea you should do a video explaning the midpoints of a triangle or just straight up math!!❤❤
@rowrow_16 күн бұрын
Finding the height of the triangle was so brilliant
@AndyMath
16 күн бұрын
It is one of my favorite logical paths. Two things are equal. Change your perspective on one of them. Learn something new.
@nimamousavi335216 күн бұрын
when simple solutions doesn't satisfy your brain needs
@juanvaldo66612 күн бұрын
Great video man. Thanks
@EchoFox7716 күн бұрын
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
@Wilba658216 күн бұрын
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.
@henrygoogle494916 күн бұрын
Wow was not expecting the flipping excitement. I made it to the end.
@jamesrocket561616 күн бұрын
Nice, I love problems involving prismoidal volume which is applicable in earthworks (excavation and backfilling of soil).
@generaleditz116 күн бұрын
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
@DanielNRollins16 күн бұрын
Exciting, as usual
@aj__stha16 күн бұрын
Shortcut method would be subtracting the smaller traingular prism with the bigger triangular prism, but this was fun as well. Thank you
@KingTurnell16 күн бұрын
I want the video about mid segmentes in triangles
@bartomiejzemsta293213 күн бұрын
What a great video 😊 wow 🤩
@robbiekavanagh280216 күн бұрын
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
@matianz16 күн бұрын
thanks andy xoxo
@ccdsah16 күн бұрын
nice numbers, did it all in my head
@yn_km15 күн бұрын
Bro you must make A lot more of these videos
@Mixa_Lv16 күн бұрын
Wow, that is a massive prism
@danpliska92416 күн бұрын
hi andy. i made it to the end of the video. great visual effects.
@maddening685016 күн бұрын
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.
@jreese828416 күн бұрын
Ah, relativity! 4 minutes isn't "long" for YT; although it's a bit long for you. Love your work!
@360_swagburittos915 күн бұрын
Never thought about the flipping triangle
@Rorablink16 күн бұрын
The hard way indeed😂 I could never
@arthhaa16 күн бұрын
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
@wubbybubby127616 күн бұрын
For the height of the trapezoid, u also coulda used the GMT theorems of similarity, immeadiately getting (h/6) = (8/10) as a proportion
16 күн бұрын
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.
@AlmightyFSM16 күн бұрын
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?
@vipcesh14 күн бұрын
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
@kmjohnny16 күн бұрын
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.
@roblowery318816 күн бұрын
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.
@TheTomTracey16 күн бұрын
Nice video length
@billiboi12216 күн бұрын
He did it the HARD way!
@vincent412l716 күн бұрын
How did we assume a rectangle with right angles, and parallel lines to make a trapezoid? (The spacing is not given for the top).
@umbra0rpng17316 күн бұрын
No views in 20 seconds... People aren't getting excited over math 😢
@bIeed12 күн бұрын
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.
@max-dd4xj16 күн бұрын
What pc program do you use for pulling out pieces of figures?
@donvito197316 күн бұрын
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.
@greendruid3316 күн бұрын
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?
@txikitofandango2 күн бұрын
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
@robertdoherty453915 күн бұрын
Video being 4 minutes and 20 seconds is absolutely not a mistake
@the_god_masterpiece16 күн бұрын
Nice 🙂
@tortinwall16 күн бұрын
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.
@mulangumundemba996216 күн бұрын
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.
@kujmous16 күн бұрын
I was not prepared for the flip.
@okalov16 күн бұрын
Area big triangle minus area little triangle multiplied by the length of the prism and you've got it
@fadil917116 күн бұрын
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-kl1me4zs1s16 күн бұрын
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)
@cowofthemonth16 күн бұрын
Just teselate the larger triangle into 9 smaller similar triangle, 1-3-5, so 3 times the smallest triangle --> 24*3*50
@notonlyhuman607316 күн бұрын
“This is probably gonna be a long video” Me looking at the vid length: nice
@Nomedecor16 күн бұрын
i did it to the end
@mrshreykumarjain16 күн бұрын
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
@Logia_16 күн бұрын
Guys he is getting stronger with each view, he is now able to interact with the math himself. :0
@prplzbr15 күн бұрын
Hey, I solved one! I did it the easy way, but still, I'm taking the win.
@VK-198116 күн бұрын
S1=(3/18)*S S=24*18 S1=3*24=72 V1=72*50=3600
@drakkondarkspell16 күн бұрын
Made it to the end.
@brandongraham350915 күн бұрын
3-4-5 triangles!
@RichardTapp116 күн бұрын
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 ...
@emanuellindstrom400316 күн бұрын
I made it to the end 😊
@hellkr16 күн бұрын
I made it to the end ;)
@dod-do-or-dont15 күн бұрын
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
@thatonedynamitecuber16 күн бұрын
I really need mid segments its so confusing
@RubyPiec16 күн бұрын
midsegment of triangle video!!!
@Peter_Riis_DK16 күн бұрын
I can spot another way, but it doesn't really seem easier. Let's have it.
@KasperDahlTangen13 күн бұрын
And the easy way: Face = triangle + parallellogram = 8*6/2 + 8*6 = 72 Volume = Face * Depth = 72 * 50 == 3600
@picknikbasket16 күн бұрын
How extending!
@aljawad16 күн бұрын
👍🏼
@KittyTittyAnonymity16 күн бұрын
4:20 best part
@davidvidic16 күн бұрын
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
@k3vi016 күн бұрын
I made it to the end.
@richieE71416 күн бұрын
I made it to the end lol
@cbl84395 күн бұрын
i made it! it was fun
@jamie870316 күн бұрын
What in the hell is the easy way to find the area of a trapezoid without knowing the height or base lengths lol
@BoolianKazooka
12 күн бұрын
Find the area of the triangular prism that has the trapezoid, then subtract the triangular prism in the very corner.
@jamie8703
12 күн бұрын
@@BoolianKazooka YOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I DIDJT EVEN SEE THAT
@maa356316 күн бұрын
Is there eaven an easier way?
@blakewright57516 күн бұрын
Made it to 420!
@YEOHWILSONMoe16 күн бұрын
4.20 minutes noice
@yepyepmusic16 күн бұрын
I've made it to the end
@AsifAli-ym2cq9 күн бұрын
4:20 length video again😂
@izme100016 күн бұрын
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.
Пікірлер: 129
Love the dramatic flipping of the triangles.
@powerzx
16 күн бұрын
I don't.
@Danymillion
13 күн бұрын
@@powerzxshut up
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
16 күн бұрын
YES, this was one of the easiest problems shown, I finished it fast. How exciting :)
@JonnyBoi957
16 күн бұрын
That is probably why the title is I did it the hard way
@z000ey
16 күн бұрын
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
We all made it to the end because of how exciting it was.
i love how he animated it also 3:03 is very cool
@bebektoxic2136
16 күн бұрын
Didn't expect that lol.
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.
People who mentally solved it while looking at the thumbnail 👇
the taming apart of the other prisms + the triangle flip TRULY made this one exciting. thanks!
Your videos have opened up so many shortcuts and concepts for me with math, I'd love a video on triangle mid segments
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.
I made it to the end, don't worry.
Yeah please make a another video on the mid segment of triangles. Im pretty hooked in!
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
Exactly 4:20 minutes, nice
@Beiconqueso02
16 күн бұрын
How exciting
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. 😛
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 KZread 🙄]. Seriously, Andy, great work....as always. 💙👍
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.
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. :)
Blew my mind with the triangle rotation
I made into the end!! Anyway yea you should do a video explaning the midpoints of a triangle or just straight up math!!❤❤
Finding the height of the triangle was so brilliant
@AndyMath
16 күн бұрын
It is one of my favorite logical paths. Two things are equal. Change your perspective on one of them. Learn something new.
when simple solutions doesn't satisfy your brain needs
Great video man. Thanks
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
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.
Wow was not expecting the flipping excitement. I made it to the end.
Nice, I love problems involving prismoidal volume which is applicable in earthworks (excavation and backfilling of soil).
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
Exciting, as usual
Shortcut method would be subtracting the smaller traingular prism with the bigger triangular prism, but this was fun as well. Thank you
I want the video about mid segmentes in triangles
What a great video 😊 wow 🤩
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
thanks andy xoxo
nice numbers, did it all in my head
Bro you must make A lot more of these videos
Wow, that is a massive prism
hi andy. i made it to the end of the video. great visual effects.
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.
Ah, relativity! 4 minutes isn't "long" for YT; although it's a bit long for you. Love your work!
Never thought about the flipping triangle
The hard way indeed😂 I could never
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
For the height of the trapezoid, u also coulda used the GMT theorems of similarity, immeadiately getting (h/6) = (8/10) as a proportion
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.
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?
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
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.
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.
Nice video length
He did it the HARD way!
How did we assume a rectangle with right angles, and parallel lines to make a trapezoid? (The spacing is not given for the top).
No views in 20 seconds... People aren't getting excited over math 😢
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.
What pc program do you use for pulling out pieces of figures?
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.
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?
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
Video being 4 minutes and 20 seconds is absolutely not a mistake
Nice 🙂
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.
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.
I was not prepared for the flip.
Area big triangle minus area little triangle multiplied by the length of the prism and you've got it
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
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)
Just teselate the larger triangle into 9 smaller similar triangle, 1-3-5, so 3 times the smallest triangle --> 24*3*50
“This is probably gonna be a long video” Me looking at the vid length: nice
i did it to the end
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
Guys he is getting stronger with each view, he is now able to interact with the math himself. :0
Hey, I solved one! I did it the easy way, but still, I'm taking the win.
S1=(3/18)*S S=24*18 S1=3*24=72 V1=72*50=3600
Made it to the end.
3-4-5 triangles!
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 ...
I made it to the end 😊
I made it to the end ;)
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
I really need mid segments its so confusing
midsegment of triangle video!!!
I can spot another way, but it doesn't really seem easier. Let's have it.
And the easy way: Face = triangle + parallellogram = 8*6/2 + 8*6 = 72 Volume = Face * Depth = 72 * 50 == 3600
How extending!
👍🏼
4:20 best part
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
I made it to the end.
I made it to the end lol
i made it! it was fun
What in the hell is the easy way to find the area of a trapezoid without knowing the height or base lengths lol
@BoolianKazooka
12 күн бұрын
Find the area of the triangular prism that has the trapezoid, then subtract the triangular prism in the very corner.
@jamie8703
12 күн бұрын
@@BoolianKazooka YOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I DIDJT EVEN SEE THAT
Is there eaven an easier way?
Made it to 420!
4.20 minutes noice
I've made it to the end
4:20 length video again😂
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.
My guy… subtract
Actually it's called a cuboid
i did
End