3. Three-dimensional figures, or solids, can be made
up of flat or curved surfaces. Each flat surface is
called a face. An edge is the segment that is the
intersection of two faces. A vertex is the point that is
the intersection of three or more faces.
5. A cube is a prism with six square faces. Other
prisms and pyramids are named for the shape
of their bases.
6. Postulate
Write the formula for the
volume of a right
rectangular prism.
V = lwh
We will assume prisms
are RIGHT from now on
15. Example 2A: Identifying a Three-
Dimensional Figure From a Net
Describe the three-dimensional figure that can be
made from the given net.
The net has six
congruent square
faces. So the net
forms a cube.
16. Example 2B: Identifying a Three-
Dimensional Figure From a Net
Describe the three-dimensional figure that can be
made from the given net.
The net has one circular
face and one
semicircular face. These
are the base and sloping
face of a cone. So the net
forms a cone.
17. Check It Out! Example 2a
Describe the three-dimensional figure that can be
made from the given net.
The net has four
congruent triangular
faces. So the net
forms a triangular
pyramid.
18. Check It Out! Example 2b
Describe the three-dimensional figure that can be
made from the given net.
The net has two circular
faces and one
rectangular face. These
are the bases and curved
surface of a cylinder. So
the net forms a cylinder.
19. Lateral Area of a Prism -
sum of the areas of the
lateral faces.
Surface Area of a Prism -
sum of the lateral area
and the areas of the two
bases
23. Prisms and cylinders have 2 congruent parallel
bases.
A lateral face is not a base. The edges of the base are
called base edges. A lateral edge is not an edge of a
base. The lateral faces of a right prism are all
rectangles. An oblique prism has at least one
nonrectangular lateral face.
24. Lateral Area of a Right Prism
Is their a short cut for
finding the lateral
area ?
25. Lateral Area of a Right Prism
The lateral area LA of a
right prism with height
h and perimeter of
base p is:
LA = Hp or L = Hp
26. Surface Area of a Right
Prism
The surface area SA of a
right prism with lateral LA
and the area of a base B
is:
SA = LA + 2B
or S =L + 2B
27. Volume
Volume equals Area of the
Base times the Height of the
object.
V = BH
Area of the Base x Height of the object