Classifying Solid Figures
Brenda Meery
Jen Kershaw
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Printed: June 12, 2016
AUTHORS
Brenda Meery
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Classifying Solid Figures
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Classifying Solid Figures
In this concept, you will learn how to classify solid figures by identifying faces, edges and vertices.
Mack is building a garden for his mother. He wants to put in pentagonal stones to decorate the area. In order to
make the best arrangement, he needs to find the number of faces and edges in a pentagonal prism. How many faces
and edges are there in a pentagonal prism?
In this concept, you will learn how to classify solid figures by identifying faces, edges and vertices.
Solid Figures
Solid figures are shapes that exist in three-dimensional space. Unlike plane figures, which have only length and
width, solid figures have length, width, and height. Let’s take a look at identifying solid figures.
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Here are three different prisms. Each figure has two common congruent bases and these bases are hexagons,
pentagons and triangles. The sides of each figure are made up of rectangles. You name these figures according
to the base: a hexagonal prism, a pentagonal prism and a triangular prism. Notice that the key with prisms is that the
sides are rectangles.
Another type of solid figure is called a pyramid. A pyramid has a base and triangular sides that meet at a single
vertex. You identify a pyramid according to its base.
Here are some pyramids.
There are other solid figures too that have circles in them. See below a cylinder, a cone, and a sphere.
Solid figures have faces, edges and vertices. You can use the number of faces, edges and vertices to identify the
solid figures.
A face is the flat side of a solid figure. Faces are in the form of plane shapes, such as triangles, rectangles, and
pentagons. An edge is the place where two faces meet. Edges are straight; they cannot be curved. Vertices or a
vertex is the point where edges meet.
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Chapter 1. Classifying Solid Figures
You can identify the three parts of a solid by looking at the following diagram.
Once you know how to identify the faces, edges and vertices of a solid, you can count them too.
Let’s look at an example.
How many faces, edges, and vertices does the figure below have?
First, let’s count the faces. Remember, each face is a flat plane shape. In this figure, the bases, or top and bottom, are
hexagons and the sides are all rectangles. There are six faces around the sides and two bases. This figure has eight
faces in all.
Next, let’s count the edges where each face meets another. There are six around the top hexagon where it meets each
side, and six more around the bottom hexagon where it meets each side. And there are six more where each side
meets another. This figure has 18 edges.
Then, let’s find the vertices. Remember, a vertex is like a corner. This figure has six corners, or vertices, on the top
and six on the bottom. This figure has twelve vertices in all.
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You can count faces, edges and vertices of all the solids. This information can also help us to classify them. If you
think about prisms and pyramids, you can think about the number of edges, faces and vertices.
However, if you think about a sphere, a cone and a cylinder, you will notice that faces, edges and vertices don’t apply
to all of these.
Let’s look at a chart to help us classify solid figures according to their faces, edges and vertices.
TABLE 1.1:
Figure Name
sphere
cone
cylinder
triangle pyramid
square pyramid
prism
Number of Faces
0
1
2
4
5
at least 5
Number of Edges
0
0
0
6
8
at least 9
Number of Vertices
0
0
0
4
5
at least 6
Let’s look at an example.
Draw a triangular prism.
First, you know that a triangular prism has two bases shaped like triangles. To draw the triangular prism, let’s begin
by drawing its base.
Next, let’s draw the side that is facing toward the front. You know that a prism has rectangular sides that are all the
same height. You also know that the bottom edge of the rectangular side connects to one edge of the base, so you
can draw the rectangular face attached to the base.
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Chapter 1. Classifying Solid Figures
Notice that the top face is exactly the same size and shape as the base, only it is connected to a top edge of the
rectangular side. Imagine you could slide the base triangle up and put it on top of the rectangle.
It becomes easy to figure out how to draw this figure once you understand that the bases are triangles and as with
any prism, the sides are rectangles. Connecting them together forms the solid figure.
Examples
Example 1
Earlier, you were given a problem about Mack’s stone pattern.
Mack needs to know the number of faces and edges on a pentagonal prism in order to build a pattern of stone in the
garden.
First, you can use the fact that n+2 gives us the pattern for the number of faces in a prism. In this pattern, n represents
the number of sides in the base. The pentagon has five sides, so we know that n is 5.
Faces = n + 2
Faces = 7 faces
Next, draw a picture of a pentagonal prism.
From the drawing, you can count the edges.
Faces: 7
Edges: 15
Vertices: 10
The answer is 7 faces, 15 edges, and 10 vertices.
Example 2
Sketch a cylinder.
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First, remember that cylinders have two circular bases. Therefore you will need to draw a circular base which is the
same as the circular top face.
Next, add the front view. Cylinders do not have a side face. They are curved. Imagine holding up a cylinder and
looking at it from the side. What would it look like? From the side, the cylinder would appear to have a rectangular
face. This is a bit of an illusion, but you should sketch the cylinder as you would see it. Even though the side meets
the base around the curve of the circle, you can draw a rectangle. But let’s show the top and bottom of the rectangular
side with dashed lines so that you know there isn’t really a straight edge there.
There aren’t any vertices to connect between the top and bottom faces since they are round, so you’re done.
Example 3
Name the figure below and name the number of vertices, faces, and edges.
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Chapter 1. Classifying Solid Figures
First, name the figure.
Rectangular Prism
Next, find the number of vertices, faces, and edges.
Vertices: 8
Faces: 6
Edges: 12
The answer is there are 8 vertices, 6 faces, and 12 edges.
Example 4
Name the figure below and name the number of vertices, faces, and edges.
First, name the figure.
Hexagonal Prism
Next, find the number of vertices, faces, and edges.
Vertices: 12
Faces: 8
Edges: 18
The answer is there are 12 vertices, 8 faces, and 18 edges.
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Example 5
Name the figure below and name the number of vertices, faces, and edges.
First, name the figure.
Cone
Next, find the number of vertices, faces, and edges.
Vertices: 0
Faces: 1
Edges: 0
The answer is there are 0 vertices, 1 faces, and 0 edges.
Review
Answer the following questions about each solid figure.
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Chapter 1. Classifying Solid Figures
1. What is the name of this figure?
2. How many faces does it have?
3. How many vertices does it have?
4. How many edges does it have?
5. What is the name of this figure?
6. How many faces does it have?
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7. How many edges does it have?
8. How many vertices does it have?
9. What is the name of this figure?
10. How many faces, edges and vertices does it have?
11. What is the name of this figure?
12. How many faces does it have?
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Chapter 1. Classifying Solid Figures
13. How many edges does it have?
14. How many vertices does it have?
15. A figure has one circular face, no edges, and no vertices. What kind of figure is it?
16. A figure has one pair of parallel sides that are circular. What kind of figure is it?
17. Sketch a cone.
18. Sketch a pentagonal prism.
Answers for Review Problems
To see the Review answers, open this PDF file and look for section 8.5.
Resources
MEDIA
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URL: https://www.ck12.org/flx/render/embeddedobject/65520
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