In this video, you will learn about pyramids. With these two examples, which are most common in tests, here you go. Let's find the lateral area, the total area, and the volume of a regular quadrangular pyramid. First, I ask you to leave your like. If you are not subscribed, subscribe to the channel. Come learn about the regular quadrangular pyramid. Let's do the two questions: lateral area, total area, and volume. Access the first pyramid. Note that the base is a square. Why did you create it? Because the word regular refers to the base. So, when I have a quadrangular pyramid, the base is a regular quadrilateral, all sides equal. Squares. Here you go. Look, six square root of two. What is the square root of two? This measurement also gives you. What is the lateral edge of the pyramid? And in this case, here I will ask you. What is the volume of the Curió pyramid? What is the volume of the pyramid? Is it always the area of the base times height over three? There is a video tip by three. It is the pyramid. It has the tip, the vertex up there. Area of the base times height over three. Here is what I need. You need the area of the base. True, the base is easy to find, right? What is the kissed side? It is the square 6 square root of two squared 6 squared 36 square root of two squared cut from two and 36 x 2 72 square cm Mayor curious, it was already the area of the base here God and it has today now I want to find What is the height how will I find height this same one that I want to pass you in the regular quadrangular pyramid and we other pyramids also regular hexagonal triangular always explore one two Pythagoras as I will do in this example and another in this one. Therefore the two figures and the height is what I want you to connect in the center to the vertex of the base and curió understand here is a right angle exactly and you will explore this Pythagoras of this red triangle I saw here is ten what lateral edge of the pyramid baby up to H is who I want and I have to find this measurement here which by the way is half of the diagonal of the square which is the base So here it is look the base is a square with side 6 root of 2 its diagonal is what if you do not remember diagonal of square L square root of two simulated is six square root of two the diagonal is six root square root of two x square root of two is here the side will be what is diagonal root of 2 times root of 2 is root of 4 which is 2 x 6 of one centimeter if the diagonal cured I understood then from the center Alberto is half of the diagonal exactly six centimeters and then you explore this Pythagoras which is this message I wanted to give you is here look Pythagorean triangle H squared + 6 squared = 10 squared right we import this squared is equal to the sum of the squares of the legs are the neighbors of the angle of 90 here it will be without minus 3664 and square root of 64 8 cm would be height curious and now substitute the eight here and solve the question perfect curió How do I do it here I can go stay there 72 by three of 24 and the volume 24 X 8 curió just do it just do it and we go to the next one it's eight times 2 16 160 8x there are 32 are 192 cubic centimeters and it would be the volume of our pyramid of the print that this Pythagoras is very important and comes to continue on this question here, let's go on this question. If I ask you what is the lateral area of Clara Total, what is the volume of this pyramid? Let's go first to the lateral area. I want to explore a very important piece of information about the lateral area, which is this triangle here. Look, VBC Cureaua. Because you gained focus on the triangle, come down because it is a lateral face and then lateral area four times this easy to obey. But how will I find it? From this basic phase, 12 times the height of the Face, which I don't know, I'll call it x. And the height of the face. The note is the apothem of the pyramid. The apothem of the pyramid is from the vertex, take it and from the Face to the midpoint of the base edge. Prefect, in which Pythagoras I'm going to explore this time, this one here. Here is the height of the pyramid. Hit the center, which is a regular quadrangular pyramid. The base is a square. Bring it to the point. And for me, beauty, that the base here of the Triangle, see, go down. Cureaua, now Pythagoras here measures 8 if everything is more than 12. Here below, half the side of the square. I bet on the square here measuring 6 there 6 8 10 generally a Pythagorean triangle here x = 10 cm right now Cureaua I'm going to find the lateral area if here it measures 10 the area of the triangle is what the base times height over two and here I simplify two by 26 X10 60 square centimeters the area of a Face but how many faces of these are equal baby be there are four Faces because if at the base there are four edges each edge and raises a lateral face then the lateral area of our pyramid will be what four times because there are four Faces four triangle the area of one of these triangles 6 x 4 24 240 cm square got and to finish Of course the volume is easy more volume area of the base what side this side 2 squared times height which is eight over three don't forget it's a third Cureaua how would you do it is I would do it like this 2 x 2 x 8 over three I would simplify that would be four and then yes I would do the product is four times 1248 x 8000 pure understand Did you send it well here the Like if you want and open the same table, it's eight X8 64, go 68 x 4 32 and six 38 384 cubic cm. Well, it's missing volume. Okay, the total area. Total area. It's definitely what the total area is. It's the lateral area, which we already found, which is 240, plus the base area, which is 2 x 12, which is 144. So, I have this sum: 388 square cm. Our total area, so we found the volume was. Total lateral, as we predicted, great. I invite you to print it out, the painting is yours, and let's go together towards the top. Organizations strategy with the Curió method. Comes with your approval. The painting is yours. So,