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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
OBJECTIVETo find lateral area
and surface area of a polyhedron,
the prism
Key TermsPolyhedron
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.
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 NetDescribe 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 NetDescribe 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
ObjectDraw 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 7.2P685 #’s 13-26 and 28-31
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.
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.
