Unit Outline 10.1 Areas of Parallelograms and Triangles (0.5
day) 10.2 Areas of Trapezoids, Rhombuses, and Kites (1.5 day) 10.3
Areas of Regular Polygons (2 days) 11.1 Space Figures and Cross
Sections (2 days) 11.4 Volumes of Prisms and Cylinders (1 day) 11.5
Volumes of Pyramids and Cones (2 days) 11.6 Surface Area and
Volumes of Spheres (1 day) 11.7 Areas and Volumes of Similar Solids
(2 days) 10.1 Areas of Parallelograms and Triangles (0.5 day) 10.2
Areas of Trapezoids, Rhombuses, and Kites (1.5 day) 10.3 Areas of
Regular Polygons (2 days) 11.1 Space Figures and Cross Sections (2
days) 11.4 Volumes of Prisms and Cylinders (1 day) 11.5 Volumes of
Pyramids and Cones (2 days) 11.6 Surface Area and Volumes of
Spheres (1 day) 11.7 Areas and Volumes of Similar Solids (2
days)
Slide 3
10.1 Areas of Parallelograms and Triangles Unit 9 Understanding
3D Figures
Slide 4
Vocabulary
Slide 5
Finding the Area of a Parallelogram
Slide 6
Find the Missing Measurement
Slide 7
Your Turn! Find the area of each parallelogram. Find the value
of h for each parallelogram.
Slide 8
Vocabulary
Slide 9
Finding the Area of a Triangle A triangle has an area of 18 in
2. The length of its base is 6 in. What is the corresponding
height? Solution: Draw a sketch of the triangle to visualize the
problem. A = bh Substitute 18 = (6)hSimplify 18 = 3h h = 6 in The
height of the triangle is 6 in. A triangle has an area of 18 in 2.
The length of its base is 6 in. What is the corresponding height?
Solution: Draw a sketch of the triangle to visualize the problem. A
= bh Substitute 18 = (6)hSimplify 18 = 3h h = 6 in The height of
the triangle is 6 in.
Slide 10
Your Turn! A triangle has height 11 in. and base length 10 in.
Find its area. A triangle has area 24 m 2 and base length 8 m. Find
its height. The figure at the right consists of a parallelogram and
a triangle. What is the area of the figure? A triangle has height
11 in. and base length 10 in. Find its area. A triangle has area 24
m 2 and base length 8 m. Find its height. The figure at the right
consists of a parallelogram and a triangle. What is the area of the
figure?
10.3 Areas of Regular Polygons Unit 9 Understanding 3D
Figures
Slide 22
Vocabulary Radius of a Regular Polygon Distance from the center
to a vertex Apothem Perpendicular distance from the center to a
side Radius of a Regular Polygon Distance from the center to a
vertex Apothem Perpendicular distance from the center to a
side
Slide 23
Finding Angle Measures
Slide 24
Your Turn! Each regular polygon has radii and apothem as shown.
Find the measure of each numbered angle.
Slide 25
Vocabulary
Slide 26
Finding the Area of a Regular Polygon
Slide 27
Your Turn! Find the area of each regular polygon with the given
apothem, a, and side length, s. pentagon, a = 4.1 m, s = 6 m
octagon, a = 11.1 ft, s = 9.2 ft Find the area of each regular
polygon with the given apothem, a, and side length, s. pentagon, a
= 4.1 m, s = 6 m octagon, a = 11.1 ft, s = 9.2 ft
Slide 28
Your Turn! Find the area of each regular polygon. Round your
answer to the nearest tenth.
11.1 Space Figures and Cross Sections Unit 9 Understanding 3D
Figures
Slide 31
Vocabulary Polyhedron A 3-dimensional figure whose surfaces are
polygons Face Each polygon of the polyhedron Edge Segment formed by
the intersection of two faces Vertex Point where three or more
edges intersect Polyhedron A 3-dimensional figure whose surfaces
are polygons Face Each polygon of the polyhedron Edge Segment
formed by the intersection of two faces Vertex Point where three or
more edges intersect
Slide 32
Vocabulary Eulers Formula The sum of the number of faces (F)
and vertices (V) of a polyhedron is two more than the number of its
edges (E). F + V = E + 2 In two dimensions, Eulers Formula reduces
to F + V = E + 1. Eulers Formula The sum of the number of faces (F)
and vertices (V) of a polyhedron is two more than the number of its
edges (E). F + V = E + 2 In two dimensions, Eulers Formula reduces
to F + V = E + 1.
Slide 33
Using Eulers Formula What does a net for the doorstop at the
right look like? Label the net with its appropriate dimensions.
Solution: Draw the net and then verify Eulers Formula. Faces (F) =
5 Vertices (V) = 10 Edges (E) = 14 F + V = E + 1 5 + 10 = 14 + 1 15
= 15 What does a net for the doorstop at the right look like? Label
the net with its appropriate dimensions. Solution: Draw the net and
then verify Eulers Formula. Faces (F) = 5 Vertices (V) = 10 Edges
(E) = 14 F + V = E + 1 5 + 10 = 14 + 1 15 = 15
Slide 34
Your Turn! Draw a net the 3-dimensional figure.
Slide 35
Vocabulary Cross-section Intersection of a solid and a plane
Cross-section Intersection of a solid and a plane
Slide 36
Drawing a Cross-section Draw the horizontal cross-section for a
triangular prism. Solution: To draw a cross section, visualize a
plane intersecting one face at a time in parallel segments. Draw
the parallel segments, then join their endpoints and shade the
cross section. Draw the horizontal cross-section for a triangular
prism. Solution: To draw a cross section, visualize a plane
intersecting one face at a time in parallel segments. Draw the
parallel segments, then join their endpoints and shade the cross
section.
Slide 37
Your Turn! Draw and describe the cross section formed by
intersecting the rectangular prism with the plane described. A) a
plane that contains the vertical line of symmetry Solution: See
board for cross-section; the cross-section is a rectangle B) a
plane that contains the horizontal line of symmetry Solution: See
board for cross-section; the cross-section is a rectangle Draw and
describe the cross section formed by intersecting the rectangular
prism with the plane described. A) a plane that contains the
vertical line of symmetry Solution: See board for cross-section;
the cross-section is a rectangle B) a plane that contains the
horizontal line of symmetry Solution: See board for cross-section;
the cross-section is a rectangle
11.4 Volumes of Prisms and Cylinders Unit 9 Understanding 3D
Figures
Slide 40
Vocabulary Volume The space that a figure occupies; It is
measured in cubic units Cavalieris Principle If two space figures
have the same height and the same cross-sectional area at every
level, then they have the same volume. Volume The space that a
figure occupies; It is measured in cubic units Cavalieris Principle
If two space figures have the same height and the same
cross-sectional area at every level, then they have the same
volume.
Slide 41
Vocabulary
Slide 42
Finding the Volume of Rectangular Prisms
Slide 43
Find the Volume of Triangular Prisms
Slide 44
Your Turn! Find the volume of each object. Round to the nearest
tenth.
Slide 45
Vocabulary
Slide 46
Finding the Volume of a Cylinder
Slide 47
Your Turn! Find the volume of each figure. the cylindrical part
of the measuring cup
Slide 48
Vocabulary Composite Space Figure A 3-dimensional figure that
is the combination of two or more simpler figures. Composite Space
Figure A 3-dimensional figure that is the combination of two or
more simpler figures.
Slide 49
Finding the Volume of a Composite Figure
Slide 50
Your Turn! Find the volume of each composite figure to the
nearest tenth.
11.6 Surface Area and Volumes of Spheres Unit 9 Understanding
3D Figures
Slide 61
Vocabulary
Slide 62
Finding the Volume of a Sphere
Slide 63
Your Turn! Find the volume and surface area of a sphere with
the given radius or diameter. Round your answers to the nearest
tenth.
Slide 64
Your Turn! A sphere has the given volume. Find its radius to
the nearest tenth. A) 1436.8 mi 3 B) 808 cm 3 C) 72 m 3 A sphere
has the given volume. Find its radius to the nearest tenth. A)
1436.8 mi 3 B) 808 cm 3 C) 72 m 3
Slide 65
Your Turn! The sphere at the right fits snugly inside a cube
with 18 cm edges. What is the volume of the sphere? Leave your
answers in terms of . The sphere at the right fits snugly inside a
cube with 18 cm edges. What is the volume of the sphere? Leave your
answers in terms of .
11.7 Areas and Volumes of Similar Solids Unit 9 Understanding
3D Figures
Slide 68
Vocabulary Similar Solids Have the same shape, and all
corresponding dimensions are proportional. Similar Solids Have the
same shape, and all corresponding dimensions are proportional.
Slide 69
Identifying Similar Solids
Slide 70
Your Turn! Are the given pairs of figures similar?
Slide 71
Vocabulary Volumes of Similar Solids If the scale factor of two
similar solids is a:b, then the ratio of their volumes is a 3 :b 3.
Volumes of Similar Solids If the scale factor of two similar solids
is a:b, then the ratio of their volumes is a 3 :b 3.
Slide 72
Finding the Scale Factor
Slide 73
Your Turn! Each pair of figures is similar. Use the given
information to find the scale factor of the smaller figure to the
larger figure. Two cubes have sides of length 4 cm and 5 cm. Find
the ratio of volumes.