Images of 3-D
What are 3-Dimentional Figures?
Why do we need to learn about them?
3-Dimentional Figures
 Solid Figures that are not on a flat plane.
 3-D Figures are seen in many ordinary objects around us.
Let me show you some examples!
Cones
Cylinders
Cubes
Spheres
Memphis Pyramid
Egyptian Pyramid
Pyramids
Rectangular Prism
What are Polygons?
Define
Closed 2-D figures formed by 3
or more line segments.
NOT Polygons
Examples
Polygon
Regular:
All sides are equal
Irregular:
All sides are not equal
Let’s Review Some Polygons
Matching
____ Quadrilateral
____ Octagon
____ Decagon
____ Hexagon
____ Triangle
____ Heptagon
____ Pentagon
____ Nonagon
A. 3 sides
B. 4 sides
C. 5 sides
D. 6 sides
E. 7 sides
F. 8 sides
G. 9 sides
H. 10 sides
Check Your Answers
Matching
B
Quadrilateral
F
Octagon
H
Decagon
D
Hexagon
A
Triangle
E
Heptagon
C
Pentagon
G
Nonagon
A. 3 sides
B. 4 sides
C. 5 sides
D. 6 sides
E. 7 sides
F. 8 sides
G. 9 sides
H. 10 sides
Moving on to
3-Dimentional Figures!
Three-dimensional figures are not flat figures. They
have length, width, and height. They are also called
solid geometric figures.
 The flat surfaces of three-dimensional figures are called faces.
 The faces meet at edges.
 The edges are line segments.
 The edges meet at vertices (plural of vertex).
Parts of a 3-D Figure
3-D
Figure
Face – The flat surfaces.
(Flat)
Edge – Where the faces meet. (Straight Lines)
Vertex – Where the edges meet. (Pointy Corners)
Base - The top and bottom faces.
face
vertex
edge
6 faces
8 vertices
12 edges
2 faces
no vertices
no edges
no faces
no vertices
no edges
Examples of 3D Figures
Prism
Triangular
Prism
Pyramid
Pentagonal
Prism
Square
Pyramid
Cylinder
Triangular
Pyramid
Named by the shape of
their two bases.
Also, named by the shape of
its one base.
Notice… the two bases have the
same shape!
The other faces are triangles.
Two bases that are circles.
The other faces are rectangles.
Cone
One vertex and a circular base.
Sphere
All points are the
same distance from
a center point.
Cube
All faces are squares.
3-D Figures
Prisms
Triangular prism
Rectangular Prism
Pentagonal Prism
Hexagonal Prism
Pyramids
Triangular Pyramid
Square Pyramid
Pentagonal Pyramid
Hexagonal Pyramid
Cylinders
Cones
Spheres
Cubes
Rectangular prism
face
edge
base
vertex
A rectangular prism has 6 faces, 8 vertices, and 12 edges.
cube
face
vertex
edge
A cube, just like a rectangular prism, has 6
faces (all squares), 8 vertices, and 12 edges.
Triangular prism
base
base
face
face
vertex
A triangular prism has five faces. Its base is a triangle.
(Notice that even when the triangular prism sits on a
rectangle, the base is still a triangle.) Two of its faces are
triangles; three of its faces are rectangles. It has six vertices
and nine edges.
Rectangular pyramid
face
vertex
base
A rectangular pyramid has 5 faces. Its base is a
rectangle or a square and the other 4 faces are
triangles. It has 8 edges and 5 vertices.
Triangular pyramid
vertex
face
base
A triangular pyramid has four faces.
All faces, including its base, are triangles.
It has six edges and four vertices.
Before We Move On Let’s Review
 What are the flat surfaces of a 3D figure called?
 Where do the faces meet?
 What are the corners (or where the edges meet) called?
 Which is the prism and which is the pyramid?
A)
B)
How do I find the faces, edges, and
vertices of a shape?
Pyramid Formula
Examples
Formula
 Faces = # of sides of the
base + # of the bases
 Vertices: # of faces
 Edges: faces+vertices-2
Faces:
Edges:
Vertices:
Prism Formula
Examples
Formulas
 Use the following formulas to
•
•
•
find the number of faces,
edges, and vertices.
Faces: # of sides of the
base + # of bases
Vertices: # of sides of the
base x 2
Edges: Faces + Vertices - 2
Faces:
Edges:
Vertices:
You Try!
1)
Shape of Base:
Name:
4)
Shape of Base:
Name:
7)
Shape of Base:
Name:
2)
Shape of Base:
Name:
5)
Shape of Base:
Name:
8)
Shape of Base:
Name:
3)
Shape of Base:
Name:
6)
Shape of Base:
Name:
9)
Shape of Base:
Name:
You Try! – Check Your Answers
1)
Shape of Base: Triangle
Name: Triangular Prism
4)
Shape of Base: Circle
Name: Cone
7)
Shape of Base: Square
Name: Cube
2)
Shape of Base: Circle
Name: Cylinder
5)
Shape of Base: None
Name: Sphere
8)
Shape of Base: Trapezoid
Name: Trapezoidal Prism
3)
Shape of Base: Hexagon
Name: Hexagonal Pyramid
6)
Shape of Base: Triangle
Name: Triangular Pyramid
9)
Shape of Base: Square
Name: Square Pyramid
You Try!
1)
Faces:
2)
Vertices:
Edges:
4)
Faces:
Vertices:
Edges:
5)
Vertices:
Edges:
7)
Faces:
Faces:
3)
Faces:
Edges:
Faces:
Vertices:
Edges:
Vertices:
Edges:
6)
Vertices:
Edges:
8)
Vertices:
Faces:
Faces:
9)
Vertices:
Edges:
Faces:
Vertices: Edges:
You Try – Check Your Answers!
1)
Faces: 5 Vertices: 6 Edges: 9
4)
Faces: 1 Vertices: 1 Edges: 0
7)
Faces: 6 Vertices: 8 Edges: 12
2)
3)
Faces: 2 Vertices: 0 Edges: 0
Faces: 7 Vertices: 7 Edges: 12
5)
6)
Faces: 0 Vertices: 0 Edges: 0
Faces: 4 Vertices: 4 Edges: 6
8)
9)
Faces: 6 Vertices: 8 Edges: 12
Faces: 5 Vertices: 5 Edges: 8
Now it’s your turn!
SHOWDOWN
CAPTAIN!!!!
Find the….
_____edges
_____vertices
_____faces
Answer
16 edges
9 vertices
9 faces
What shape am I?
I am a solid figure that has a circular base.
There are 2 faces in all.
There is only 1 vertex
There are no edges.
What shape am I ?
I am a…..
Cone
Find the….
_____edges
_____vertices
_____faces
Answer
9 Edges
6 vertices
5 faces
What is the name of a three-dimensional
figure with six square faces?
a.
b.
c.
d.
pyramid
cube
solid
edge
How many edges does a square
pyramid have?
a.
b.
c.
d.
4
5
7
8
I am a three-dimensional figure with five faces. My base
is a rectangle; my other faces are triangles. I have five
vertices and eight edges. What am I?
a.
b.
c.
d.
rectangle prism
rectangular pyramid
triangular prism
triangular pyramid
How many edges does a square
pyramid have?
a.
b.
c.
d.
4
5
7
8
How many vertices does a rectangular
prism have?
a.
b.
c.
d.
12
8
6
4
Which of the following has a base that
is a triangle?
a.
b.
c.
d.
Triangular prism
Cube
Square pyramid
Rectangular pyramid
I am a three-dimensional figure with four faces.
All of my faces, including the base are triangles.
What am I?
a.
b.
c.
d.
rectangular prism
triangular prism
triangular pyramid
rectangular pyramid
How many faces of a cube are
squares?
a.
b.
c.
d.
2
4
6
8
Sally is going to build a table for her family room. It is in
the shape of a triangular prism. What shapes will she
need to build the table?
a.
b.
c.
d.
5 triangles
2 triangles and 3 rectangles
2 triangles and 4 rectangles
6 rectangles
Euler’s Formula
We use Euler’s formula to check to see if all of our calculations
are correct!
Faces + Vertices – Edges= 2
If your numbers are correct, every time you plug them in it
will equal 2!
What in the World are Nets?
What do you think of when
someone mentions a net?
Maybe you think of these?
Orange Roughy anyone?
(New Zealand)
Cold water coral reef.
Let’s talk about,
NETS in MATH! ! !
Definition:
A Net is a 2-dimensional
pattern that you can fold
to form a 3-dimensional figure.
Example:
Figure 1
Figure 2
Challenge:
Which of the nets can be
folded to form a cube?
Hint:
Think about how many
faces a cube has!
A net is a 2-D pattern
like
A 2-D sewing pattern
That forms a 3-D solid shape
Forms a 3-D outfit
Let’s learn a little more about a 3-D net.
http://www.virtualnerd.com/geometry/surface-areavolume-solid/introduction/three-dimensional-figure-fromnet
Let’s practice identifying a 3-D figure from a net.
Prism or Pyramid?
Identify the 3-D figure from the net.
Prism or Pyramid?
Identify the 3-D figure from the net.
Prism or Pyramid?
Identify the 3-D figure from the net.
Identify the 3-D figure from the net.
Identify the 3-D figure from the net.
Identify the 3-D figure from the net.
Match the letter to the number.
A. ____
B. ____
C. ____
D. ____
E. ____
F. ____
G. ____