 Oh, there it is. Sweetness. Excellent. We see this image. Gang. Oh, yeah. I'm going to share the link in chat so everyone knows it. We got a link. We got an image. Here's the image. I'll post that. You know what? I'm going to pin this as well because I'm going to make sure we have the link in the description of the video when we upload it. So let me just draw this gang. I'm going to bring up the chat just in case I'm missing something. You guys can correct me on the stuff. Weird. Oops. Weird sloping square. Weird sloping. But it's not... Yeah, it's just a prison. It wasn't a... Yeah, this one's... Here, let me draw this to you. I'll give you a little lowdown before we do this, right? So the question is... What was the question again? I'm going to bring out a better pen. What color do we want? How do I calculate the volume? Been told that I should split the square into a rectangle. No, you don't need to do that. I'll show you how to calculate the volume without having to split everything up. But you can, yeah. Sure. Triangular, prison, compute the volume for each, then add them together. Yeah, basically. So basically the question here is let's do light blue. New pen. Let's see how this works. So the question is geometry related, right? And we have the following shape. And then we'll draw the same thing in the back, and then we'll connect them up. My 3D drawings are the same size. Let me bring up... Let me take a look at it from what you guys see. Oh yeah, I got a little mutated piece here. Let's correct it a little bit here. We'll correct it a little bit. I don't know if that's much better, but a little bit, I guess, right? None of my drawings are to scale. Not to scale, not to scale here. We'll flatten this guy up, too, or raise this guy up as well. Those make it more pretty anyway. At least make those parallel, sort of, right? Mr. RoboDope, good afternoon, Chicha. Unfortunately, I have to run to the gym, but looking forward to watching later. Have a nice day, everyone. You too, as well. Have a great workout, Mr. RoboDope. Work hard. Make sure you replenish and drink fluids and have a little bit of protein to build back your muscle ASAP, right? So, here's the dimensions of this thing. Oh, I keep on closing that thing. Here's the dimensions. What have we got? We've got 1.3 meters. 1.3 meters on the top of the height. We've got 1 meter here. We've got 2 meters here. 2 meters here. And we've got 0.5 meters here. 0.5 meters here. Now, the way it works is we don't need anything. We don't need any other information for that thing, so I'm going to bring it down. The diagram itself in the picture states that it isn't actually drawn, so it doesn't have to be perfect. So, not to scale. If that's 0.5, then 1.5 would have been a little bit bigger than this, or 1.3 would have been a little bit bigger than this. So, take a look at this thing. Think about geometry in the following form. Start off with a point. All shapes consider it, and we're thinking we live in a four-dimensional world. One of the dimensions being time, but we live in a three-dimensional, spatial-dimensional world. So we have this way, we've got up and down, and we've got in and out. So those are the three dimensions that we have, and this is a three-dimensional object, so it's got three directions. But start off with a point. Let's say you have a point. A point in space has zero dimensions, 0D. It's not 1, 2, 3, 0D. It's before we get into the dimensions. So this is 0D, and this is a point in space. 0D has no units either. And then you can take your point, stretch it out in one direction, and you have a line or a distance. And this is in one direction, hence it's one directional, 1D. And then you can take your point, start off the point, start a point, draw a line, go a certain distance, and then take that line, the distance, and zoom it up. You've got this. What you have here now is two directions. Remember, this was one direction, this is one direction, and this is the other direction. Now we've got 2D, two directions, and this is a surface or an area. Surface or area. It could be a map or whatever it is. So if you want to find the area of this thing, you measure this distance and then you scan this up. It's just like a scanner. It goes up. That gives you the area. And the way you do that is you multiply this times this. That's how you do it. You multiply the two directions together. As long as they were 90 degrees. If it's not 90 degrees, then form it like an area a little bit. But you're still really just multiplying the two directions together. Go along this way and go zoom up. Then you get the area. Start off with the same point. Make a line, take that line, turn it into a surface. Now you have an area of something. That's what this is, an area. And then what you can do, if you want to go in a third direction, let's say this thing now is a box. So you have one direction, you've got two directions, that's this guy and this guy, and then you've got three directions. So if you've got 3D, that means you're multiplying three different directions together. And visually, the way it works is you start off with a point, generate a line, take this line, scan up, you've got a surface, take the surface, scan in. Go along this distance and you've got a volume. That's a surface, you've got a volume. You've got a 3D shape or prism, if you want to think about it. Prism, well prism can exist, you can calculate the area of a prism or something, but let's just call it volume. As now with three dimensions, we can occupy any point in space. And now with three dimensions, we can occupy any space. We can occupy the whole space if we want to think about it that way with the volume. So for this, what you need to do is, you don't necessarily need to, because this is a prism. And by the way, any shape like this is called a prism where one surface appears on the other side, where you can just scan it in and you generate a three-dimensional object. So for example, you could have a triangular prism. There's your triangle and then zoom it into the page and you get a prism. You can get a cylindrical prism, create a circle and then zoom that circle in and you get a cylinder. So this shape appears on the other shape just by tracking along this dimension. This shape appears on the other side as long as you track along here. So over here, right? I call the triangular prism a tubular problem. A bar, yum, dark chocolate one is the best. First time chat, how are you doing? Swiff, swath, not sure if I'm going to say that. What you wrote, right? A free Julian Assange game. Free Assange, free Assange, free Assange. Publisher and journalist, that has been crucified for trying to be transparent in accountability of capitalist, power, humanity. For more information, see wikileaks.org, defend.wikileaks.org or our Julian Assange and WikiLeaks playlist on sensor 2. And if you need those length, you can come to our chat anytime you want on Twitch and type in exclamation mark. Free Assange, right up here. And what I just said with the links will appear, right? Just a little sidetrack from doing a little mathematics, because this is very, very important, very, very important, right? Now, this that we have here is a prism, right? Because this shape appears on the back side, right? Now, if, for example, this distance was smaller than that distance, you couldn't consider it a prism, right? For example, if this was, this distance here was let's say 0.75, then you couldn't consider this a prism because this length was longer than this length. So you couldn't just scan in one side to get the other side, right? But they are the same. They told us that by saying it was a prism. Okay? So all we really need to do is find the area here and multiply it by this, which happens to be 1, and that will give us our volume, right? So our issue right now is we're not really going to calculate two volumes and add them together. We're going to calculate two different areas and add them together. Now, there are formulas for shapes like this, right? That you can do, right? Calculate, but because we have these distances, we can actually, we don't need a special formula beyond a rectangle and a triangle because what we can do, we can take this thing, let's transpose the shape here, right? So we took this, right? The surface that we're looking for, the surface that appears on the back side, right? And we made a work area for us. And it's okay to do this. You don't have to cram everything on here, right? Do your work. Spread your work out if you need to, right? Don't spread out your train of thought, though. If you're working the problem of mathematics, keep it orderly, okay? First time chat. Wall bottle, yes. Let's free him so we can try. You're not very informed. You're not very informed. Put it right by yourself. You're not very informed. What's your name? Wall bottle? You need to find some other sources of information. Now, I highly recommend you don't get involved with politics too much, really. If you've been fooled by the propaganda, I think you should stick with mathematics personally. Build up the critical thought process a little bit. Wouldn't a formula for any shape be derived from splitting the shape into triangles and rectangles? 100%. Or circles, and circles as well, right? Or spheres or whatever, right? So what we do is put down the links here. So this is 1.3, that's that guy. This is 2, that's that guy. This is 0.5. Now, one thing that you notice, I'm not putting in the units anymore, because they're all the same units. In the final answer, you're going to include the units, right? So how are we going to break this up? The simplest way to break this up, the only way right now for this shape, we can really break it up, is to go start here, and come along here. Oh my God, my line is wiggly. Trying to go slow on a whiteboard is difficult. Isn't the formula for circle derived from splitting the circle into an infinite number? Yeah, then you need calculus. We're trying to stay away from the calculus aspect of it. Keep it simpler, right? So all we do, we just say, okay, there's one more level, one more formula we need, which is a circle, which is two more formulas, the circumference of a circle and the area of a circle, right? 2 pi r and pi r squared, right? So we don't have to go into the calculus level. Now, what we got here is, this is 0.5, so this has got to be 0.5, right? Easy peasy. If that's 0.5, then we got this guy. We know what this is, right? 0.1.3 minus 0.5 is 0.8. 0.8? 0.8, right? So this part is 0.0. I'll put it on the other side. So this part here is, oh, I got a little small eraser. This point here is 0.8. This is 0.8. 0.8, right? Okay, cool. And this we know is 2, right? Easy peasy. So area of a rectangle, area of, let's call this 1, area of 1 is length times width, length times width, which is length and width, I guess, 2 times 0.5, which is equal to 1. What are the units? 1 meter. Okay. What's an area of the second shape, which is a triangle? Well, area of a second shape is really area of a rectangle divided by 2, right? If you break this in half diagonally, you get a triangle. It's the same deal as this, right? Same deal as that, but we only want half of it. So we can go this times this divided by 2, because we just want half of it. So, Joe, to go back to your question, the area formula, even the triangle, comes from this, right? So this is going to be 1.5 length times width, or they call it base times height. They change the letters around. So they go 1.5 base times height. There is the base, there is the height. So it's going to be 2 times 0.8 divided by 2, 2 kills 2. So this area is 0.8 meters, and then this was 1. So this is 1, and this is 0.8. That's the total area of this duvaki. So total area of this duvaki is 1.8. This is 1.8. That's the area of this duvaki. How do we figure out the volume of this thing? Well, we multiply 1.8 by 1. So 1.8 times 1 is equal to 1.8. The area was meters squared. I should put meters squared, meters squared, my bad. So meters squared for the area, for the volume, because you're multiplying by another meter, is meters cubed. So the total volume of this thing would be 1.8 meters cubed. Slayers are things that I understand all this. Cool. I was just struggling to visualize how 1.3 creates a triangle. So we see here, right? That's how it creates the triangle. You eliminate this part from this, and you've got yourself a triangle here. Look, gang, when it comes to geometry, it's pretty cool. It's just my experience from working with a lot of students over the last two plus decades, 25 years or so. There are some kids that might not be good in some of the other algebra, like just doing simple algebra or hard algebra. It doesn't make a difference, right? But they do phenomenal with geometry. And then there are people who are really good with algebra that have a hard time with geometry. There are some people that have a hard time visualizing the stuff. They have a harder time just seeing how it looks. That's why, in my personal opinion, any math test you write, or any math test that's given to anyone, when there's work problems, they should also have a drawing of the work problem, right? Because English is not everyone's forte. If you're going to test them for their math abilities, you shouldn't be testing them for their ability to translate from English to the language of mathematics. If it is, then you should specify that is one of the requirements for the exam, for the course.