3-D Solids and Polyhedrons

3-D Solids and Polyhedrons

Geometry - Ms. Chodnowsky

• ​A polyhedron is a closed three-dimensional figure made up of flat polygonal regions.

• A face of a polyhedron is a flat surface on the polyhedron​

• ​An edge of a polyhedron is a line segment where the faces of the polyhedron intersect.

• ​The vertex of a polyhedron is the intersection of three edges of the polyhedron.

• ​The bases of a prism or cylinder are the two parallel congruent faces of the solid.

• ​The base of a pyramid or cone is the face of the solid opposite the vertex of the solid.

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​A prism is a polyhedron that has two parallel congruent bases, connected by parallelogram faces.

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A pyramid is a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex.

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A cylinder is a solid figure that has two congruent and parallel circular bases connected by a curved surface.

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A cone is a solid figure that has a circular base connected by a curved surface to a single vertex.

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A sphere is a set of all points in space equidistant from a given point called the center of the sphere. A sphere has no faces, edges, or vertices.

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​Polyhedra, or polyhedrons, are named by the shapes of their bases.

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A polyhedron is a regular polyhedron if all of its faces are regular congruent polygons and all of the edges are congruent. There are exactly five types of regular polyhedra, called Platonic solids because Plato used them extensively.

Multiple Choice

What shape is this?

• Cube
• Triangular Prism
• Rectangular Pyramid
• Cone

Multiple Choice

What is the name of this shape?

• Rectangular pyramid

• triangular pyramid

• square prism

• triangle prism

Multiple Choice

What is this shape?

• cone
• pyramid
• rectangular prism
• cube

Multiple Choice

What is the name of this polyhedron?

• Square Pyramid

• Rectangular Prism

• Triangular Prism

• Triangular Pyramid

Multiple Choice

The flat side of a 3D shape is called:

• vertex
• face
• edge
• street

Multiple Choice

The lines of a 3D shape are called...

• edges
• outside
• faces
• vertices

Multiple Choice

What shape is this?

• Cube
• Triangular Prism
• Rectangular Pyramid
• Cone

Multiple Choice

What is this shape?

• cone
• cube
• pyramid
• sphere

Multiple Choice

What is the name of this polyhedron?

• pyramid
• cube
• cylinder
• prism

Multiple Choice

What is a polyhedron?

• A many sided flat figure 
• a type of pokemon 
• a solid whose faces are all polygons
• all 3D shapes

Multiple Choice

What is a prism?

• a polyhedron that has two parallel, identical bases
• A 3D shape with a point at the top
• polyhedron that has one base
• a square box

Multiple Choice

The arrow is pointing to a ________.

• Edge
• Vertice
• Face

Multiple Choice

The arrow is pointing to a ________.

• Edge
• Vertice
• Face

Multiple Choice

What is a pyramid?

• a polyhedron that has two parallel, identical bases
• a place where fancy cats live
• three dimensional figure is a measure of the amount of space that occupies
• a polyhedron that has one base and goes to a vertex

Multiple Choice

What is the name of this polyhedron?

• hexagonal pyramid
• pentagonal pyramid
• pentagonal prism
• hexagonal prism

Multiple Choice

This is a...

• pentagonal prism
• rectangular prism
• pentagonal pyramid
• hexagonal prism

Multiple Choice

Identify the shape:

• Triangular Pyramid

• Square Prism

• Triangular Prism

• Square pyramid

Multiple Choice

How many Platonic Solids are there?

• 2

• 5

• 6

• 4

Multiple Choice

What is another name of Cube?

• Tetrahedron

• Hexahedron

• Octahedron

• Icosahedron

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EXAMPLE 1:

The solid  is formed by polygonal faces, so it is a polyhedron. There is no base, but the solid has  8 equilateral triangular faces, so it is an octahedron.

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It has:

​8 faces

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0 bases

​

​12 edges

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​and 6 vertices.

Multiple Choice

How many faces does Dodecahedron has?

• 5

• 10

• 20

• 12

Multiple Choice

A platonic solid is made up of regular, congruent shapes.

• True
• False

Open Ended

Identify your shape, whether or not it is a polyhedron, and the number of bases, faces, edges, and vertices.

E

"My shape is a ________, it (is/is not) a polyhedron, it has ___ bases, ____ faces, ____ edges and ____ vertices."