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OBJECTIVE
To find lateral area
and surface area
of a polyhedron,
the prism
Key Terms
Polyhedron
Altitude
Lateral Area
Net
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.
A cube is a prism with six square faces. Other
prisms and pyramids are named for the shape
of their bases.
PostulateWrite the formula for the
volume of a right
rectangular prism.
V = lwh We will assume prisms
are RIGHT from now on
VocabularyPolyhedron- A
geometric solid with
polygons as faces.
NEW DEFINITIONPrism-A polyhedron
with two polygonal
bases that are parallel
and congruent.
Right Prism - lateral edges
are perpendicular to the
planes of the bases.
VocabularyAltitude of a Prism - any
segment perpendicular
to the planes
containing the bases
with endpoints in these
planes. ( same as
HEIGHT)
VocabularyNet - a figure that can be
folded to enclose a
particular solid figure
ClassworkDraw a net for a right
triangular prism.
Draw a net for a right
pentagonal prism.
Classwork
Classwork
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.
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.
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.
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.
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
Classwork
LATERAL AREA
SURFACE AREA
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.
Lateral Area of a Right Prism
Is their a short cut for
finding the lateral
area ?
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
Surface Area of a Right
PrismThe 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
Volume
Volume equals Area of the
Base times the Height of the
object.
V = BHArea of the Base x Height of the object
Find the LA
Find the SA
Lateral Area of a Right Prism
Find the lateral area LA
of a right prism with
height 10cm, if the
base is a regular
hexagon with side
3cm.
Find the surface area
SA of a right prism
with height 10cm, if the
base is a regular
hexagon with side
3cm.(round answer to
nearest hundredth)
Example 1: Drawing Orthographic Views of
an Object
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.
Example 1 Continued
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.
Bottom
Example 1 Continued
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.
Example 1 Continued
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.
Check It Out! Example 1
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.
Check It Out! Example 1 Continued
Classwork/HomeworkPractice and Apply 7.2
P685 #’s 13-26 and 28-31
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