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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.
002 s.a.  of prisms
A cube is a prism with six square faces. Other
prisms and pyramids are named for the shape
of their bases.
Postulate
Write the formula for the
volume of a right
rectangular prism.
V = lwh
We will assume prisms
are RIGHT from now on
Vocabulary
Polyhedron- A
geometric solid with
polygons as faces.
NEW DEFINITION
Prism-A polyhedron
with two polygonal
bases that are parallel
and congruent.
Right Prism - lateral edges
are perpendicular to the
planes of the bases.
Vocabulary
Altitude of a Prism - any
segment perpendicular
to the planes
containing the bases
with endpoints in these
planes. ( same as
HEIGHT)
Vocabulary
Net - a figure that can be
folded to enclose a
particular solid figure
Classwork
Draw 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
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
Volume
Volume equals Area of the
Base times the Height of the
object.
V = BH
Area 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/Homework
Practice and Apply 7.2
P685 #’s 13-26 and 28-31

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002 s.a. of prisms

  • 1. OBJECTIVE To find lateral area and surface area of a polyhedron, the prism
  • 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
  • 8. NEW DEFINITION Prism-A polyhedron with two polygonal bases that are parallel and congruent.
  • 9. Right Prism - lateral edges are perpendicular to the planes of the bases.
  • 10. Vocabulary Altitude of a Prism - any segment perpendicular to the planes containing the bases with endpoints in these planes. ( same as HEIGHT)
  • 11. Vocabulary Net - a figure that can be folded to enclose a particular solid figure
  • 12. Classwork Draw a net for a right triangular prism. Draw a net for a right pentagonal prism.
  • 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
  • 30. 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.
  • 31. 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)
  • 32. Example 1: Drawing Orthographic Views of an Object Draw all six orthographic views of the given object. Assume there are no hidden cubes.
  • 33. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes. Bottom
  • 34. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes.
  • 35. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes.
  • 36. Check It Out! Example 1 Draw all six orthographic views of the given object. Assume there are no hidden cubes.
  • 37. Check It Out! Example 1 Continued
  • 38. Classwork/Homework Practice and Apply 7.2 P685 #’s 13-26 and 28-31