How to find the volume of a right-triangular prism.

We have to solve this. We have to find the volume of the right triangular prism above. That is the first thing you need to know. What type of prism is this? It is a right triangular prism. That should be the first thing that comes to mind, right? Okay, if this is a right triangular prism, That means the base of this prism is this. This place. That means this is how it is supposed to be. To stand on this right-angled triangle. That means the base is what? This particular place. So it's supposed to stand like this. If I'm to draw it properly now, it's supposed to stand like this. Then this base should be a right angle. I don't know how to draw it. But it's supposed to be something like this. You understand? I'm not good at drawing. This one is supposed to be something like that again. So this right angle here is supposed to at the base. All right, we're by this place, which is your right angle. This 13 cm is supposed to be to be somewhere here. Then you have the other parts of the right angle as 10 cm. I'm just giving you an insight, okay? It means the height is 16 cm, because if you stand it upright, That means the height is what? This 16 cm. So how did we get that? We paid attention to what They wrote. They said a right triangular prism, which means that the base is what? The right angled triangle. Now, listen and pay attention to see why I emphasize what the base is, and how will it help us find what? The volume of this particular shape that we drew. Alright, when you have a prism, the formula for finding the volume of a prism is what? Area. Volume. Okay, let's write the solution first before we start, right? There's volume. Of what? A prism. The volume of a prism is equal to what? The area of the base or base area. The base area. You have your base area times the height. Base area times the height. Now, What is the base? The base is what? The right triangle. This right triangle. Now, what is the base? area of a right triangle? Area of any triangle is what? Half base times height. Right times This particular height. That is the height of the prism right now. Half the base times the height What is it? The area of the base, which is what? The area of this triangle here. So that means That's what we are now focusing on: finding the area of this base. Now, we have that the area of the base is half base times height. So that means half times what is the base of this right angle triangle? Is this 10, right? This is the base. Ten times what is the height? Now, this is the height, and the height of this triangle is not given to us. So we are looking for this. hedge. To obtain this hedge, we are going to use what? The Pythagorean theorem. So, Let me draw this out. Let me leave this first. Let me draw out this right angle here so that We can get the height. This is what we have, and we have here to be what? 13 cm. This is our right. Angle. This is the hedge we are looking for, and this is 10 cm. Now, how do we obtain this hedge? You know that according to the Pythagorean theorem, the side facing this right angle is called the hypotenuse, and the Pythagorean theorem states that this side, which is opposite the right angle, And for the longest side of this triangle, that's when you square it—that's 13 squared, okay? That it is equal to the sum of this squared plus this squared. So it's going to be h squared. plus 10 squared. That is according to the Pythagorean theorem. Now, we are looking for what? H squared. So I want this h squared to be by itself. So this plus 10 squared, we move across to become minus 10 squared, right? To become minus 10 squared. So we are going to have 13 squared minus 10 squared because this plus, we change to minus, is equal to h squared. Now, 13 squared Minus 10 squared is going to give us what? First of all, 13 squared is 169, okay? So we have 169. minus 10 squared is what? 100. 100 is equal to h squared. Okay, if you have followed me to this level, it means that you are actually enjoying what I'm doing. So please, I will ask you to subscribe at this point and also turn your notification bell so that anytime I upload a new video, you will be notified so that you can join me as well. Alright, please do that so that you don't Miss me in my next video. Now, how do we get our 169 minus 100? That will give you what? 69 is equal to h. squared. That means for us to obtain our h, we need to take the square root of both sides. Right? So it means that, look at what we have here, that 69 equals h squared. Therefore, our h, That means the square root of h squared will give us h, right? Is it equal to the square root of what? 69. Now, this implies that our h is equal to, what is the square root of 69? Okay, the square root of 69 will give us 8.3066. 8.3066, let's call it 8.3066, let's leave it like that. So this means that our h is What? 8.3066 centimeters. Now that we have that, we can now comfortably determine what? Our base area and we can now solve this. So let's go ahead and solve it. Permit me to clean this once more. Let I'll just put everything in order, okay? So that means that, that means that the volume of this The volume is equal to what? Base area, base area times what? The height, okay? Now we said that the base area is what? Half the base times the height, times this height here. Now this is equal to half times, our base is what? 10, okay? Over 1 times, our height is what we just found, which What is it? 8.3066. 8.3066 times, we can say over 1. Our height, that is the height of the prison. Remember I told you that when you stand it properly, this place is supposed to be underneath because it's a right-angled prison. So it's supposed to be under. That means this becomes our height. This It's the place that will be like this. So our height will be 16 cm. So let's go ahead and solve. So it means our volume is what? 5 times 8.3066 times 16. And when you enter that Your calculator, your answer will be. So let's go ahead and multiply this. 5 times 8.3066 times 16. You are going to have 664.5. 664.5 cm³. And this becomes your answer. Thank you for watching, and see you next time. Bye.