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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will know how to identify polyhedrons and you will become familiar with the common types of polyhedrons found in the world. You will also see real-world examples of polyhedrons in action.

In this lesson, we talk about polyhedrons. **Polyhedrons** are 3-dimensional solids with flat faces. Each side of the polyhedron is a polygon, which is a flat shape with straight sides. Take the cube, for example. It is a polyhedron because all of its faces are flat. Each face of the cube is a square. If you play board games, then you are probably playing with a cube in the form of dice. Most houses are also polyhedrons because all the faces are flat. Any object that you see whose faces are all flat is a polyhedron.

Now, let's talk about some common types of polyhedrons.

The cube that we just talked about is also a **platonic solid**, a special type of polyhedron. A platonic solid is a polyhedron whose faces are all the same. Look at the cube, and you will see that all its faces are squares, and each face is the same as all the others.

In the world, there are only five platonic solids. The first is the tetrahedron made up of four faces that are all triangles. The second is the cube made up of six faces that are all squares. The third is the octahedron made up of eight faces that are all triangles. The fourth is the dodecahedron made up of 12 faces that are all pentagons. And the fifth is the icosahedron made up of 20 faces that are all triangles.

The next type of polyhedron is the prism. **Prisms** are 3-dimensional solids that have flat faces and two identical ends. The cross section along the length of the prism is all the same. The most common prism that you will see is the triangular prism that you use in science experiments where you break up white light into a rainbow of colors. You can see that it has two faces that are both triangles. The other faces are rectangles. If you cut anywhere along the length of this prism, you will get the same triangular cross section.

You can have prisms with differently shaped ends. The cube, surprisingly, is also a prism. We call the cube a square prism because its ends are square. The cross section of a square prism will always be a square. If the ends are pentagons, then you have a pentagonal prism.

Another common type of polyhedron is the pyramid. A **pyramid** is a 3-dimensional solid whose base is a polygon and whose sides are all triangles that all meet at the top. You might be most familiar with the famous pyramids of Egypt. These pyramids have a base that is square with triangular sides that all meet at the top.

Just like with the prisms, you can have different kinds of pyramids. If the base is a triangle, then we call it a triangular pyramid. If the base is a square, then we call it a square pyramid. If the base is a pentagon, then we call it a pentagonal pyramid.

Now, let's review what you've learned. **Polyhedrons** are 3-dimensional solids with flat faces. A **platonic solid** is a polyhedron whose faces are all the same. There are only five platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. **Prisms** are 3-dimensional solids that have flat faces and two identical ends. A **pyramid** is a 3-dimensional solid whose base is a polygon and whose sides are all triangles that meet at the top.

When you are finished, you should be able to:

- Recall what a polyhedron is
- Explain what a platonic solid is and name the five types
- Describe what a prism and a pyramid are
- Recite the different types of prisms and pyramids

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- What is a Polyhedron? - Characteristics & Examples 3:08
- Types of Polyhedrons 3:32
- Front, Side & Top View of 3-Dimensional Figures 4:55
- Nets of 3-Dimensional Figures 3:09
- Planes and the Polyhedron: Definition and Example 3:52
- What Are Platonic Solids? - Definition and Types 4:39
- Prisms: Definition, Area & Volume 6:12
- Pyramids: Definition, Area & Volume 7:43
- What Are Cylinders? - Definition, Area & Volume 5:09
- Cones: Definition, Area & Volume 8:59
- Spheres: Definition, Area & Volume 5:22
- Go to 6th-8th Grade Geometry: Polyhedrons & Geometric Solids

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