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### Course: 6th grade (Illustrative Mathematics)>Unit 1

Lesson 8: Lesson 13: Polyhedra

# Recognizing common 3D shapes

Learn about 3D shapes! A square pyramid has a square base. A rectangular prism is a box shape with all rectangular sides. A triangular prism has triangle faces on opposite sides. A sphere is like a globe. A cylinder looks like a can with circular faces on top and bottom. Shapes are fun!

## Want to join the conversation?

• what is a vertice?
• A vertex (vertices is the plural of vertex) is a point where the sides of a shape intersect. So basically any corner on a shape is a vertex.
• how do i find surface area
• You find the area of each side of the object and then add them all together.
• Would a shape with an octagon for a base and triangles for sides meeting at a point be called an octagonal pyramid?
• Yes,an octagonal pyramid is a pyramid with a base that's a polygon with eight sides, or an octagon, and triangular faces, or sides, that meet at a point directly above the bottom.
• What kind of polygon have 100 sides ?
• Think of a century as 100 years, so it would be a centagon. This is like a decagon is like a decade (10 years).
• At , Sal says "This has sides that are triangles", doesn't he mean faces?
• I think he means bases.
• The Rectangular prism is also called a Cuboid. True or False?
• That is true. A rectangular prism is also called a cuboid. A cuboid is a three-dimensional shape that has six faces, all of which are rectangles. A cuboid is also a right prism, which means that its bases are parallel and congruent, and its lateral faces are perpendicular to the bases. A cube is a special case of a cuboid, where all the faces are squares. However, not all rectangular prisms are cuboids. A rectangular prism can also be oblique, which means that its bases are not aligned one directly above the other, and its lateral faces are parallelograms2
• A sphere is a circle right?
• It may seem that way, but technically, a sphere is a 3-D shape (has width, height, and depth) and a circle is 2-D (width and height) A circle is missing the depth needed to become a 3-D shape. Also, you find volume for spheres and area for circles. This then changes the formulas.
Circle: A = pi*r^2
Sphere: V = 4/3*pi*r^3
Good luck in your journey through geometry!
• It is fun doing stuff like this :)
• I don't know what a vertice is
• what the differences between vertices and edges?
• A vertex is where two or more edges meet, so a vertex is a point and a edge is a line segment.

## Video transcript

- [Narrator] So I have five three dimensional shapes over here, and I also have five names for them. And what I want you to do is pause this video and think about which of these shapes is a square pyramid, which of these is a rectangular prism? Which one is a triangular prism? Which one is a sphere and which one is a cylinder? All right, now let's just work through this together. And really this is just something to know because some people in various subjects will sometimes throw out these words. So first let's start, let's think about which one is the square pyramid. So this shape here on the right clearly looks like a pyramid. And the thing that makes it a square pyramid is the idea that its base is a square. Let me see if I can shade this in. So the base of this right over here is a square. So that's where the square pyramid comes from. If it's a triangular pyramid, then the base would only have three sides, but this is a square pyramid. So let me move this over there. So that is a square pyramid. All right, let's do the next one. Which one is a rectangular prism? A prism you can view as a three dimensional object. And since it's saying rectangular prism, well the best one here that is rectangular, notice this shape right over here is rectangular on every side. And it's three dimensions. It is a prism. And so this is the rectangular prism. So let's move that over. So that is our rectangular prism. Now, triangular prism, so this one is interesting. If you look at this shape right over here, it has sides that are triangles. You see this up here is a triangle. And you see this down here is a triangle, although they're connected by these rectangular sides. And this is actually what's called a triangular prism. In a square pyramid, the faces which are triangles all meet at a point. In a triangular prism, you have two opposite facing sides that are triangles. And you'll see all of these in different orientations, in different, you know, sometimes it'll be resting like this, sometimes it'll be on its side. But this is a triangular prism. Let me- so that is a triangular prism. And so we have two left. You might be able to figure these out. Which one is a sphere? Well, when I think sphere, I think of like a globe. And so this choice right over here is clearly a sphere. So let me move that over. Let me move it over. Okay, so that one is a sphere. And then last but not least, a thing that looks like a can is a cylinder. So let me move that over. So that is a cylinder and we're all done. And so these are just useful names to know for shapes. Cylinder is, you're connecting, you have these two faces that are circular and then they're opposite each other. It's kind of like a triangular prism. But instead of having these hard edges, 'cause you have a triangle, you have a base that is a circle and a top that is a circle.