1. Drill GT Geom 5/7/14
Find the unknown lengths.
1. the diagonal of a square with side length
5 cm
2. the base of a rectangle with diagonal
15 m and height 13 m
3. the height of a trapezoid with area 18 ft2
and bases 3 ft and 9 ft

4. OBJECTIVE
To find lateral area
and surface area
of a polyhedron,
the prism

5. Key Terms
Polyhedron
Altitude
Lateral Area
Net

6. 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.

8. A cube is a prism with six square faces. Other prisms
and pyramids are named for the shape of their bases.

9. Postulate
Write the formula for the
volume of a right
rectangular prism.
V = lwh
We will assume prisms
are RIGHT from now on

10. Vocabulary
Polyhedron- A
geometric solid with
polygons as faces.

11. DEFINITION
Prism-A polyhedron
with two polygonal
bases that are parallel
and congruent.

12. Right Prism - lateral edges
are perpendicular to the
planes of the bases.

13. Vocabulary
Altitude of a Prism - any
segment perpendicular
to the planes
containing the bases
with endpoints in these
planes. ( same as
HEIGHT)

14. Vocabulary
Net - a figure that can be
folded to enclose a
particular solid figure

15. Classwork
Draw a net for a right
triangular prism.
Draw a net for a right
pentagonal prism.

16. Classwork

17. Classwork

18. 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.

19. 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.

20. 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.

21. 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.

22. 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. Classwork

24. LATERAL AREA

25. SURFACE AREA

26. 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.

27. Lateral Area of a Right Prism
Is their a short cut for
finding the lateral
area ?

28. 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

29. 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

30. Volume
Volume equals Area of the
Base times the Height of the
object.
V = BH
Area of the Base x Height of the object

31. Find the LA




32. Find the SA




33. 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.

34. 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)

35. Example 1: Drawing Orthographic Views of
an Object
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.

36. Example 1 Continued
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.
Bottom

37. Example 1 Continued
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.

38. Example 1 Continued
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.

39. Check It Out! Example 1
Draw all six orthographic views of the given object.
Assume there are no hidden cubes.

40. Check It Out! Example 1 Continued

41. Classwork/Homework
Practice and Apply 7.2
P685 #’s 13-26 and 28-31

42. 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.

44. A cube is a prism with six square faces. Other prisms
and pyramids are named for the shape of their bases.

45. 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.