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.
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
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.
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.
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
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 RU-vid 🙄]. Seriously, Andy, great work....as always. 💙👍
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. :)
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.
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
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.
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
16 дней назад
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.
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.
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
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
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
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.
